TITLE: Getting nervous refereeing a paper
QUESTION [43 upvotes]: I am refereeing my first paper and I'm quite excited! But inexperienced and I would like to ask an advice to the Maths Community of MO. Let me tell you that I have already read Refereeing a Paper, but it seems that my question is quite different. Roughly:

What is the point after which you get nervous while refereeing a paper?

Specifically:

I've found many English mistakes. (Well, I'm not a native English and so I can understand. So I am not nervous yet)
I've found some maths inaccuracies like "let A be any set"... and then I have discovered that the proof of the first result works only for finite sets. (OK, those are only inaccuracies - I am not nervous yet)
There are many references like "we use the notation of [X]", "this result is proved in [X]", where [X] is a BOOK, without specifying a precise section, or the number of the result... should I get this book and read all to find out the correct references? - just thinking of it, makes me a bit nervous..
(most importantly). There is a mathematical more serious mistake. Something that might be fixed, but not obviously (my definition of obvious is three evenings, in this case). I am not saying that the paper is completely wrong but that now... now I'm getting nervous!

Now, taking into account that the person who asked me to referee this paper told me: be selective, we accept only 20% of submitted papers, 

what should you do in these cases? Reject? Ask for a revision? Not getting nervous and try to see if the rest of the piece is good (I'm quite a good guy and I'm doing that at the moment)?

Of course I will talk with the editor, but I also would like to know more opinions that might be helpful in future.
Update: Thank you very much to everybody for the numerous and helpful comments.
Valerio

REPLY [13 votes]: I like the comment of Francis Crick in `What mad pursuit' that one should always start a referee report with praise, but of course not hold back on the detailed criticism. 
I have found that a referee can also help the author by asking for clarification in the Introduction of the aims of the paper, what does it accomplish in relation to previous work in the area, and what questions are still open. The author may also not have got the title right in relation to the expectations of readers: some of my early papers had lousy titles which not not convey easily what was in the paper. 
It is useful to know that the referee is not responsible for the correctness of the paper: that is the responsibility of the author. Of course, if the referee has doubts on the correctness,  these must be raised. 
I am unhappy about remarks such as "there are doubts about the interest of this area", since some papers are of interest precisely because they go against the so-called `mainstream', which, to mix a metaphor, flaps about like a sail in a gusty wind. 
The job of referee is very important, and I wish you luck and interest in this.