à l'université (même si l'université est indéterminée. « l'université » est considéré ici comme un collectif)

Are you sure? (you probably are, it's your mother tongue, but I have to ask).
Here it's a university which we don't know its name, just one of many. How would you distinguish between it and "at the university"?

I read your comment once more, and I see what you mean.
D'accord, corrigé.

je sais que ça paraît étonnant, mais ce n'est pas ambigu.
On dira, en général, « je suis/je vais à l'université »
et précisément « je suis/je vais à l'université Paris IV »

mais on ne dit jamais : « je suis à une université »

I can understand that. Actually, although I'm not a native French speaker, I couldn't write this sentence from the first place (it sounded too strange to my ears), so I Googled it before posting it to Tatoeba. As I found quite a few hits, I thought that maybe it's acceptable with francophones, in spite of what I thought.

I guess a few Frechmen would say it but that would be marginal and it is incorrect in any case. The problem is, we find almost everything on the Internet. You name it. Our own translation mistakes are being indexed by search engines and are subsequently used by other people as references...It's just a nightmare! The end of reference...

I'll tell you, in some instances, mistakes outnumber correct forms and it's not just on the Internet. For instance, in France, more people prononce « Les haricots » as if there was a "z" in between the two words, although it is wrong, since « haricot » starts with a "h aspiré" so no "liaison is possible. That is actually one of the criteria in France to assess the level of education of people. If you pronounce « Les haricots » incorrectly, it betrays that you haven't got very far in terms of "Lettres"...This only, could determine your fate...
English works according to usage by the masses, so if a mistake is frequent enough, it becomes the rule, and that is what happens all the time. Mistakes do rule. Not all languages work this way, far from it.
Alas, most English speakers tend to suppose that all languages must work the same way as English so they tend to trust the Internet...

I have been reflecting a lot about this since I started working on Tatoeba. And I think the problem is getting worse and I don't see a solution...
Bad words chase good words, the same way bad tender chases the good one...In the case of tender, we know it since the antiquity, in the case of words, it just became visible since English started to be spoken in America and it becomes really obvious now with the Internet...
Ultimately, I think incorrect sentences will outnumber correct ones in every language on Tatoeba. It's just a matter of time...

Is there some kind of academy for modern Hebrew, or is it left to usage (I doubt that...)?

First of all, unfortunately, I have to agree with you - to everything that you said (wrote) above.

Yes, there is a Hebrew Academy (the Academy of the Hebrew Language), but not all Israelis abide by its decisions. For instance, I run several internet forums in Israel. One of them is about linguistics and world languages. People who write there almost always ignore certain decisions of the Academy; when new surfers drop by and ask how to say a certain word, or whether a certain form is correct or not - the almost unanimous reply there is "if you say it like that, then it's correct". I'm the only one (almost) who usually adheres to the decisions and recommendations of the academy. But I don't always do that. Sometimes, as other Israelis, I stick to forms that seem to me more acceptable. All in all, the Academy is usually perceived as a body which is a bit detached from the people, and whose decisions more often than not are not adopted by most of the people right away.

I should add, though, that in Hebrew, as in other languages, there is the spoken, everyday language, and the standard and elevated registers. So, you can use lower-standard words or forms of speech, and more literary forms. However, it's not like in Arabic, where there is a dichotomy and the language sort of split into two diverse dialects.

But the thing is, if say, you write contracts in Hebrew, are there no risks of ambiguities? If so, how is the matter resolved?
In French, if you use non-official French words in your contracts, your contracts may simply be void, because the administration recognizes only official French and if the opposing party says a clause is non-French, it is void.
So, people may say whatever they want about academicians being detached from the people (which actually is not true, because all french academicians are famous writers and people of culture who are read by many French people who subsequently share their language form...After all, not everybody is a demiurge who can claim language creation: What we read shapes our language!), at the end of the day, the Academy will prevail, because French law (judicial, constitutional, administrative, fiscal) is written and is written only in official French that subsequently percolates to lawyers, private contracts, businesses, justice and...every individual.
Official academic French is also the only form that is taught in French schools, by about 1 million teachers, whether private or public. If they don't teach official French they would have their teaching licenses removed. That simple.
I'm always having fun at youngsters who claim they don't give a damn about the old academicians. 20 years later and 10 ephemeral word-trends later, they use academic words and that's that! There are actually very few exceptions. Academicians are in the world and they actually understand it much better than most of us when it comes to language.

Don't worry, contracts are written in official Hebrew, more or less according to the rules of the Academy of the Hebrew Language. Official documents are still written in the official, standard register and other elevated registers.

But the younger generation, especially in talkbacks etc, uses colloquial Hebrew, slang forms, distorted forms etc.