Applying for post-doc, how to mention mutual acquaintances?
I'll answer with a view from the other side (I.e. as a recruiting professor). Getting mention of a mutual acquaintance in an application email (or cover letter) is not so common. Most often, I find out about those from reading the CV (former student of mine was PhD advisor, for example) or by getting a separate recommendation (or follow-up) by email directly from our mutual friend.

But, I did recently receive such an application mentioning a common acquaintance, and I must admit it was a nice touch. I definitely will bring up the subject with said acquaintance in the net future, checking for his views on the candidate.

The wording was "light": "I heard a lot of good things about your research group by XXX, who is an officemate in my current group".