I keep lots of my questions in my favorites for various reasons, some of them are closed or highly down-voted questions. I hope I am not giving the impression to the OPs that they are good questions. If this is the case then I would switch to use the browsers favorites.
It's hard to say what impression it gives, since this is pretty subjective...
That said I think it's pretty clear to those that understand the site that this doesn't mean that you think that it is a good question - that's what upvotes are for - but that you want to keep track of the question (for whatever reason - improved searching, updates and answers, etc.)
On the other hand, there are badges that encourage favorited questions, so I'm not sure what that tells you...
Speaking from a purely utilitarian perspective, starring a question is more convenient than doing it in the browser. Unless you have an elaborate browser-synchronization scheme, that is. Starred questions remain with you wherever you go, on all devices.
As for sending a signal to the OP. there's no clear way to read what a star means, unlike an up- or downvote. Please also note that stars are not anonymous, so downvoting and starring after a short interval may eventually (next Sunday) leak your vote through SEDE (dunno about the API).
Just my $0.02, but I tend to favorite/star questions based on their value, or relevance, to me without regard for what the OP thinks; I mean that in a respectful way. I would guess most SE users do the same in regard to favorites, but I could be wrong. I also agree that it's hard to quantify how someone feels when their question is favorited because it is very subjective.
That being said, I think it's a great question you've asked because it truly made me look at my process/system for using favorites and if I need to revaluate it.
I personally favorite questions that interest me in a way or an other. Sometimes the question is not that interesting in itself but if one of its answers mention something interesting (let's say something I do not know) I favorite the question.
This is said, there are two badges:
- Favorite Question: Question favorited by 25 users
- Stellar Question: Question favorited by 100 users
So you favorite a question if it interests you. You are interested in good but not bad things. So personally I am convinced you are giving the OP the impression his question is interesting after all.
I think that unexperienced users will be confused by that only if other feedback is lacking. If all questions of a particular user are heavily downvoted or closed without any comments/comments that make no sense, then he may feel "bashed" by the community without reason, especially if someone favorites his questions (because that may give him the impression to beeing an underdog/asking question that people think are stupid but are secretly great). That means if a question is bad and no constructive feedback on improvement or errors were given yet, you should consider giving a little bit of feedback on what the question is lacking, to avoid misunderstandings.