Try to find work as a copy editor. You might enjoy it.

Generally, fact checking is for fact checkers, not translators. I try to point out to the client whatever obvious errors I run into, but it's not my job to actually look for them.

Yes, that degree of thoroughness does reduce the amount you can translate per hour. I work at the high(er) end of the market, and I feel the higher rate reflects the fact that I put in this extra researching time.

I always point out factual errors (or any suspicions thereof) politely, including typos in the German original text. In the past I have pointed out that names are wrong (Lolyd could well be Lloyd), dates are implausible (2989 etc) and that art works do not belong in the place mentioned because I know they are owned elsewhere.

If I find no Internet (or other) evidence of a fact or name I ask clients to double-check it, and if necessary explain it to me. My experience is that authors and publishers are inevitably grateful for this interest in detail, even if the fact turns out to be accurate after all. I am not interested in working for clients who are not interested in accuracy themselves. And next time they are consequently more likely to choose me again...

Does anyone know what the legal situation is, I mean, if something is obviously wrong for anyone to see, can you get sued for damages for translating without pointing out the mistakes?

I seem to remember having heard that as a translator you have no legal obligation to point out mistakes. You are given a text to translate and, unless you specifically have a pre-arranged editing function as well, it is not your job to analyse the rights and wrongs of the text. But the usual disclaimer here: I'm not a lawyer (nor do I specialise in legal translations!) and therefore don't know for certain. I think if you failed to point out something obvious about the source text, and it then got published, your client might be a bit miffed and not give you the next job (while at the same time recognising that it was his/her own mistake in sending a less than perfect source text and that there is no legal basis for compensation).

I have only ever been thanked for pointing out errors and, depending on the text, they are not all that hard to find. A few times a logical mistake has not been accepted as such by the author, but at least I felt I mentioned it. I would never check a bibliography however, unless I was being paid to do so.

Currently I work for a large insurer where we translate medical files and legal documents with no access to the authors (doctors, wills, etc.)
When a mistake is obvious, we translate as written with a [sic] directly behind it. In other words, we "flag" it. Yes, we see the mistake, but it is not our position to correct it.
As far as errors in grammar go, well, it seems to me you render it in the best grammar/language (keeping the same language level) possible in the target language, unless it is a direct quote of some sort, which should then be placed between quotation marks anyway.

I have done the same thing in freelance situations where there was no access to the author.

I can only confirm that clients are usually happy when content problems are pointed out, but how to make them value this part of the job?
as i translate art texts for print publications, i am often unravel highly complex sentence structures -only to discover that grammar and content simply do not add up. sometimes i feel concepts are shrouded in complexity to detract from a want in logic and clarity. then i find my self interpreting the meaning and translate/edit/rewrite it accordingly. sometimes it is hard to draw the line. as i enjoy research and editing, i state this angle to the job and also make it clear in my invoice, dividing it into research/translation/edit/copy/telephone time. and i always highlight changes i have made and ask for approval (which is seldom denied).
recently i was translating a art uni website. they were introducing a series of new courses, all with their own unique titles. returning a collection of 12 words with an invoice listing several hours might come as a shock to clients. i find if you involve your client in the selection process by disclosing your preliminary research -or poetic brain storming!- thus giving them a better understanding of the time you have invested. also you give your client a chance to state preferences, which can be very helpful!