I'm interpreting your question to be about suboptimal design decisions that became popular somewhat by accident and were then unchangeable due to backward compatibility concerns.
Have more than 32 bits of IP address space.
Rewrite some old fundamental protocols, like BGP (routing) and SMTP (email), to have better security (authentication / encryption).
Make the browser's low-level language be an efficient bytecode-based compiled language like Java, rather than an inefficient dynamic language like JavaScript (although JavaScript is less inefficient than it used to be, thanks to recent improvements in JS engine technology).
Allow web pages to separate data from formatting without requiring Javascript or server-side technologies.
Use Markdown as the language of the Web instead of the XML-based HTML.
Cross-browser vector graphics support.
Decentralize DNS and SSL (perhaps using Namecoin or the like?)
Make domain names read left-to-right instead of right-to-left.
>Make the browser's low-level language be an efficient bytecode-based compiled language like Java, rather than an inefficient dynamic language like JavaScript (although JavaScript is less inefficient than it used to be, thanks to recent improvements in JS engine technology).
Not every use case for javascript demands native-level performance or strict type safety, though. You would really rather have a separate, compiled binary for every time someone wanted to alter the DOM on their page? And break the ability to view the source and edit in the browser?
I can see the case for replacing javascript with a saner interpreted language, but we've already tried Flash-based sites and Java applets and for the most part the result has been slow, bug-ridden, insecure proprietary nightmares.
markdown is a fuzzy, fragmented, primitive light-markup.
but +1000 on the generalized suggestion for light-markup.
and instead of all the inane complexities of html-plus-css,
use a model to give a good default display of the content,
but let the user reformulate the display quickly and easily.
(the "zoom" nonsense is the wrong way to go about things.)
to sum up: it should be easy to put something on the web,
and easy for people to format viewing to their preference.
*
create collaborative-filtering to separate wheat from chaff.
it's more than slightly embarrassing that it's now 2014,
and we _still_ haven't done this obviously needed task.
once we saw we could store-and-forward everything freely,
it was immediately clear the haystack will grow infinitely,
and thus there is a huge need to be able to isolate needles.
*
people have always saved and treasured family photographs...
we need to facilitate that human need, and save our history.
*
build in an objective search engine and sharing modalities,
so that hundreds of billions of dollars -- literally! --
aren't siphoned out of our pockets to google and facebook.
*
put advertisers in their place -- i.e., the yellow pages.
keep their ugly noisy pollution out of our public spaces.
*
make those "public spaces" a collection of _private_ spaces,
so i'll retain ownership of, and control over, _my_ content.
*
build in the necessary mechanisms for intelligent discourse,
and reasoned public action, to deal with vital issues in the
social, political, economic, cultural, and ecology arenas.
*
automate hum-drum work to the greatest degree possible.
elevate societal appreciation for those doing hum-drum work
we are unable to automate. garbage-collectors are heroes,
just like fire-fighters; the internet can frame-and-praise.
encourage those who are so-inclined to become _artists_:
painters, poets, programmers, musicians, writers, whatever.
our _creativity_ is the only thing that can save us humans
from our extinction, which will soon stare us in the face.
*
strive to integrate the offline and online worlds, so we can
eliminate hunger, poverty, and homelessness. _yes,_we_can._
the rich can stay rich, but nobody should be poverty-ridden.
(and if you say these issues are unrelated to the internet,
you don't get it, and really should pay better attention.)
*
while i'm at it, stop letting the rich boys use the miracle
of the internet as another one of their weapons to wage war.
*
comfort the afflicted, and afflict the comfortable.
(if the shoe fits, wear it, because this does mean you.)
Well, I bet those that are nit-picky will still correct others like
+ It's "Ask HN" not "Ask"
+ Come on man, grammar, "If we could erase all of the"
+ Were you too lazy to put a space after the comma? "over,how" {Add some other insults here}
+ You sound a lot like someone in Brazil, it should be "how would it look like?" rather than what you have there.
But then there are those that shrug and move on, not wasting their energy or frustration on such silly little things (with their help).
I expect that web developers would panic initially at the loss of all their documentation--but they are now aware that graphics designers and typographers have existed this whole time and recreate grids and other things.
Standards would definitely come out with different quirks, but probably not as much as IE6 brought (and kept) to the market.
I'm going to reject the premise of this question, because I think it will lead to disagreement. I think you first need to ask what goals would a redesigned internet seek to fix/maximize. Would we be designing for increased security, with some sort of key exchange embedded into low-level protocols? Would we be designing for lack of control, where no country or corporation can gain undue control over a large part of the infrastructure? Would we be designing for future-proofing, to minimize the impact of migrations to improved protocols? Or would we focus on other problems that people feel exist in our current implementation?
Basically, there are a lot of things that people consider problematic about the internet, but not everyone agrees on that. Following the GRPI model (http://www.businessdictionary.com/definition/GRPI.html), we'd first need to align on the goals for this project. To skip right to the end result will result in people solving different problems and arriving at very different results.
Personally, I think the three areas I identified above are the most important goals for the redesign. I think core protocols, whether low-level, like TCP, or higher, like SMTP, should be designed to require encryption. I'd want to remove centralized organizations like ICANN and even well-behaving organizations like IANA and the regional registries. I don't know if its possible to prevent consolidation of internet infrastructure, like the long-haul backbones, but we could optimize protocols for mesh networks and local connections to make it as easy as possible to avoid last-mile monopolies.
One of the technologies that I think we could learn from would be BitCoin. While I'm not really in favor of it as a currency, you could use a similar strategy as a replacement for DNS registrations and IP assignments. With a large enough address space, you could simply "mine" the addresses you'd want to use in the same way that BitCoins are mined. And domain names could be mined in the same way. The blockchain would be huge, but you'd have a way to issue a signed route to your IP address.
I think the scenario would be caos. Lots of governments have invested in this, if you suddenly make a "erase and reset" I expect a really financial caos.
Then, probably a very big regression in terms of technology: no data, no services. We have to start gathering them all over again. To exemplify: no Google Maps, no Weather data, phone directories, etc. Think all these things we must gather again.
Assuming what's installed on personal computers is not erased as well, we have a pretty serious dilema in front.
In this escenario, I suspect companies would start over, and everyone will fight to be the first Google, building all those technologies that were successful for the company. And so on.
It would look pretty much like it did in the mid 80s: fragmented, proprietary and designed to be monetized. Microsoft would have an internet, Google would have an internet, Amazon would have an internet, and they wouldn't directly interoperate. Both sides would gleefully charge subscribers to access another internet, and the interoperability wouldn't be complete. The technical and market forces that allowed TCP/IP become the de facto starting in the late 80s/early 90s would be fought tooth and nail, should they even recur. DRM would be built into the lowest level of the protocol stacks.
Or put another way: mobile phone app stores, which to a large extent are a pretty concerted effort to reinvent solutions to the problems solved by the world wide web.
Have more than 32 bits of IP address space.
Rewrite some old fundamental protocols, like BGP (routing) and SMTP (email), to have better security (authentication / encryption).
Make the browser's low-level language be an efficient bytecode-based compiled language like Java, rather than an inefficient dynamic language like JavaScript (although JavaScript is less inefficient than it used to be, thanks to recent improvements in JS engine technology).
Allow web pages to separate data from formatting without requiring Javascript or server-side technologies.
Use Markdown as the language of the Web instead of the XML-based HTML.
Cross-browser vector graphics support.
Decentralize DNS and SSL (perhaps using Namecoin or the like?)
Make domain names read left-to-right instead of right-to-left.