Is it common to have exam questions 'peer reviewed'?

Yes; as mentioned in the UK it is expected that assignments (usually those greater than a certain proportion of the overall mark) is both internally checked and externally checked before being sat by students.

I have acted as an external examiner involved in the checking of the exam papers of another university. It is a valuable role that experienced academics can play in both improving the student experience, and the quality of the learning and teaching of an institution.

Another aspect that is also worth mentioning is post-exam error checking. In my department (some considerable time ago) we did an experiment of random error checking and to our astonishment, discovered that despite the diligence of the most experienced marker, things got missed. Our checking showed up whole missed script pages, ridiculous arithmetic errors in the final score and whole class transcription errors where spreadsheet cells were "off-by-one". As a result more regular clerical checks were done on everyone's marking and result recording to gain much in quality and student satisfaction.

This seems to be very dependent on location. I think it is a good idea, but in the US, at least, it seems to be very uncommon. Lecturers might need to have exams looked at by a more senior faculty member in some institutions, but mostly the faculty is trusted to get it right.

In some institutions that teach very large classes, exams may be created by a "committee" consisting of the main faculty member and a few senior assistants. This gives some assurance against gross errors. In such places you can also have some of the TAs take the exam under exam-conditions. This gives both an indication of overall difficulty and helps guard against ambiguous or misleading phrasing.

Much less common, of course, is to have exam questions statistically validated prior to use. It is very difficult to do such a thing of course unless the exam questions are national in scope and can be trial tested under experimental conditions.

Very common in my experience. just to note I am in Switzerland...

And even if it is not prescribed by the university, common sense does seem to get most of my colleagues in the past to ask one to "have a look at x" on an ad hoc basis. We tended to do this for each other, even before "moderation systems" were "forced upon us" or the existing relationship was made more formal...

This, simply, helps to avoid typing errors, or number errors ie a factor of 10 missing that can make a really good question such an issue for students who are under stress...

Part of moderation can be where external moderators from other institutions come in to evaluate a particular course, where they speak to the lecturers, the students and check the exams and answer scripts for consistency.

On a personal note, I did not like being externally moderated at first, but now value the process for a different view point as I have found the people who come in face the same problems with classes / students that I do. So, the discussion tends to be "I'm considering this" and the response is " Well, interesting, worth a try, but look out for this or this". It makes a difference which I now value...

I remember a Professor, where I did my studies, who was told to write an "open book" exam for his course. So he duly did so... Sent it in for external moderation (the so-called experts as mentioned in another answer...) and the moderator could not complete the exam... :) The moderator had to ask for the solutions... My lecturer continued with the original style of exam not going to open book....