Well here goes 'nuthin - Disclaimer: I am a SharePoint Administrator and consultant. I see a few things reading though this thread, but I will hit your responses.
We do have an administrator, now internal. Originally we were using an outside vendor.
Sounds like what you had was a guy that kept the lights on, and the new guy isn't much more. As a rule of thumb outside SharePoint(SP hereafter) work is running about what mid to top tier SQL work is running. In other words, though I know cost != competence the checks to the outside vendor should have at least pinched petty hard. Capable SP Admins/Consultants are relatively rare, they know this and charge accordingly. My bet is those checks didn't pinch, thus my statement.
Either way, I'm not sure how the administrator could be responsible for the embarrassing kludge that is the Office-Sharepoint "integration". It is so clearly a bolt-on afterthought to the whole office suite that I'm a little surprised I have to defend my position.
Your SP Admin is partly at fault, from your post it sounds like your SQL Admin, Domain Admin, and network guys all need to get on boeard with making this work right.
...Try copying a folder with a few thousand files in it to Sharepoint...
Ah - there is a training issue, and a setup issue at once. If you are trying to use SP as it is intended there are very few cases where you would move several thousand files at once. SP has the ability to look into and use file shares, let them live where they used to. There also seems to be a setup issue with SQL in any event, my bet is that the guy who installed it didn't optimize the SQL instance, and yah, if you are new to the game there are some big holes to miss.
Every once in a while, it simply fails to save the document you are editing silently. The result is that people make a local copy to work on and then upload it as a new version manually...
I guarantee this is a setup issue where the domain admin didn't give enough leash to the SP admin to do his job. When it is being set up you pretty much have to have the domain admin cede some control to the SP admin for the time it takes to set the thing up, . Guess what almost never happens.... It sounds extreme I know, but you have to get some latitude to do things right. Without knowing the specifics I would bet there are timeout issues or network permission issues. When setup right the integration reallly is that good but the big bugaboo is training.
I don't find the searches to be any better than the Twiki searches were with the Google appliance.
Well, to be honest, one thing I tell people is that SP search administration is almost a job unto itself (and certainly is over a certain size SP install). It also comes back to training (yeah I know I am sounding like a broken record here). It can dig into all sorts of things and index them for search, but without the proper meta data surrounding each item it isn't anywhere near what it can be. So if people aren't properly constructing their meta data ...
Yes, the admin will remove them when I request... sometimes. Apparently some of them are big security problems when hosted on a "trusted" internal site so he won't unblock all of them.
That is just a well weird way to say that. (no offense intended). The only "trust" comes from the web browser. If you can't download .exe's off of your browser then that really isn't a SP issue. Also SP keeps a single list of what it will and will not host. That list by default is restrictive as you would hope it would be, but it is editable. Our local SP happily hosts .bat and .exe files without issue. Hell, the .bats launch right from the browser.
So to sum up, it sounds like you have had two relatively inexperienced SP admins who aren't getting the cooperation they need from their IT counterparts to get things set up right and because of it you have a bad taste for SP in your mouth. Honestly, it happens. SP is a **huge** beast of software that even MS doen't see the whole picture on sometimes. Some things it does very very well, and some it just sucks at but it sounds like you have had a bad run in with what are supposed to be the good parts. I put that at the feet of your SP Admin, and whoever was in charge of roll out / education.
SP is a wily beast and not easy to admin sometimes. If I can offer any advice I would be glad to help out (and no I am not looking for a gig, I have too much work as it stands).