A lot of it is the general, philosophical way the organization works and how it looks at codes, and what it believes it's purpose is. I do think ICC does some things really right - the fundamentals of building the code(s), educating and certifying the competence of users, partnering with other industry stakeholders, etc. But the weight of their mistakes can sure sometimes overshadow the good - at least for me.
There are a fair amount of things that need fixed:
The copyright/protectionism nonsense should go away first. All the codes need to go on the website, including all of the legacy codes, and they should all be in a free to access and
use (read: copy and pastable) format for gov't. members. The argument is that "we lose too much money", blah, blah, blah. Not-for-profit means that I don't care. If ICC can't figure out a way to break even (you know, the responsibility of all not-for-profits) without charging their members twice for the same material, then perhaps they need to look at where they're spending money. The business should not be built around selling pdf's to members who have already paid a dues fee and/or bought paper books. Charge me a fee to sell me a book to recoup the cost of printing it, but don't charge me
$800+ a year to use that same code on my computer when it didn't/doesn't cost a dime to upload it to the website. I might be persuaded that charging a
very minimal fee, for the
actual cost of getting it to the website, could be charged, but I'm not sure I'd even go for that. The cost is so minimal (or should be) as to be insignificant. Raise everyone's dues just a dollar a year and you've more than covered it.
The intellectual property argument is flawed IMO as well. When ICC publishes a brand new version of a code then sure, it's copyright protected. I can get on board with that. But the whole reason for ICC to exist is for local governments to
adopt those codes. Once the very first unit of gov't. adopts that new version, then that code is no longer anyone's property - it is a law of one of the United States. Restricting access to a law is fundamentally wrong. Again, a minor argument for recovering
actual costs of providing access to it could be made, but that's it.
Next fix is the IT department. Is the website done in-house or is it an outside firm? Either way, what do we have to do so we can start all over? The website is a disaster, and has gotten steadily worse since I've been using it. It was at least navigable 4 or 5 yrs. ago, but every "upgrade" since then has been worse and worse. I could tell you everything that's wrong with it but I'd be here all day... As a minor example; just this week, they've changed the login procedure 3 stinkin' times.

There comes a point where you just have to put it out of its misery. I wouldn't save a thing about it - scrap it all and start from the beginning.
And then - ICC loves its committee's, right? So next is forming a committee that might accomplish some good - the Code Reduction Committee. Their only job would be to recommend to the membership which code sections (or even, gulp!, entire codes!!) to get rid of/remove/delete/eliminate. Go through every book ICC puts out, line by line, and get rid of all the $%!t that doesn't need to be there. All anybody is interested in nowadays is adding more, more, more, and making things more difficult to get to the end of a project. Politics aside, the "get rid of two regulations for every one new one" is close to the greatest idea I've ever heard from a gov't. official. If we want the construction industry to grow (which keeps all of us, and everybody at ICC, in a job), we should definitely be embracing that mindset and the philosophy behind it. Just because the code(s) are getting bigger doesn't mean they're getting better.
While we're on committee's, we can eliminate/consolidate some of the rest of them. Did you know that there are 43 committee's currently listed on the (crappy) website committee page?
43!?!? And some of those committee's have their own committee's!? Every time each one of them meets/travels/does any kind of business, ICC spends money. It's crazy. I mean really, a rainwater collection committee?

Wouldn't most people believe that the already-existing plumbing committee could take care of catching water in a barrel? Giving every single interest their own committee at some point becomes counterproductive, and just adds to the artificial bloat of all the codes.
Once we get all that sorted then we can move to a 5 year code cycle, to get us out of this constant race to upgrade/fix/change/repair/add new to the codes that we're in. It might even give a few locals time to get caught up, so maybe we won't have me enforcing one version, the next town over another version, and the County still another. Wouldn't it be cool to have a minute to breathe between adopting the current code and when the next one comes out? And I don't think "rapidly evolving materials" or technology or whatever is a valid argument against this, either. There is an "engineered design" clause in all the codes - if materials/technology outgrows the codes in those 5 years, surely the engineered design can account for the difference. I'm sure the engineers would tell you it can!
And then after all that, we can get started on the voting methods/procedures/eligible voters/etc., the Annual Meeting/Code Hearings themselves, the certification/testing/ceu procedures, the plan review office, the affiliate companies, etc., etc., etc. And I haven't even started yet on where ICC should be most publically involved, which is with their chapters in Statehouses in all 50. I can't think of a single valid reason why, if an ICC chapter is lobbying for or against something in their Statehouse, that an ICC rep is not standing beside them.
Edit: After reading all that again, I think everything here could be applied to NFPA as well (save for the last couple sentences about chapters and staff). They don't do it any better than ICC, so it's not an ICC-exclusive set of issues.