Q:

Is checking the format of a paper an expected part of the reviewing process? 

I have some papers to review and I am wondering whether I should do an in-depth inspection over the whole paper format?  I see nothing major but there might be some tiny format errors here and there.. 

Does the organizing committee expect reviewers to check submissions
  against the conference format? 

A:

I would say the responsibility of the reviewer is to judge the content of the paper.  So, checking if the format of the journal/conference has been followed is not part of this job.  Very large and obvious deviations can be pointed out, but for example spotting that the font of the caption is in size 11 and not 10 is not part of a reviewers task. 

A:

In general I agree with the other two answer but somehow in every paper that I have ever received a review for there has been some sort of comment on something formatting related from at least one of the reviewers.  These have ranged from suggestions for changing the fonts of the formula or captions to spotting that font for footnotes should be 9 instead of 10 for that journal etc.  
I think there is some sort of a code that if you find something you don't neglect it and ask for correction but in general that's not your job and you don't actively seek them you just "catch" them. 

A:

Reviewers check content.  Copy editors, prior to publishing, check format and adherence to publication style guides.  
Your Milage May Vary based on the expectations of your committee.   If you have a question about what you are supposed to be checking don't be afraid to ask. 