Interjection. Self-conscious vocalism, indicating skepticism; um. “Here’s a report on the, erm, incident from CBC’s nightly national newscast.” (Slap Shot blog, New York Times, November 29, 2007) /”Justice Breyer asks a hypothetical question that he will pose several times today: ‘Imagine a well-educated American woman marries a man from a foreign country X. They have a divorce. The judge says the man is completely at fault here, a real rotter. The woman is 100 percent entitled to every possible bit of custody and the man can see the child twice a year on Christmas Day at 4:00 in the morning.’ (Erm. Isn’t that once a year?)” (Dahlia Lithwick, Slate, January 10, 2010)
notoneoffbritishisms.com 
Also “um” and “er”. But I’m not sure “scepticism” quite covers it, it’s a humorous way of ridiculing something, meaning something like “hold one a minute, I hate to say it, but come on, that’s obviously ridiculous/stupid”.
The first several dozen times I encountered it, I thought “erm” was a variant of “Erma,” as in Erma Bombeck.
Well said, Harry. My sense is that there is a difference in the way this word is pronounced in U.S. and U.K. Here it’s “um”–there, to me ears, it’s “em” (subject, I’m sure, to regional and class variations). I’m curious as to how it got from (spoken) “em” to (written) “erm.”
I think it’s pronounced more like “burn” without the R (as British accents are almost all non-rhotic). Looks absolutely ridiculous in print though, especially in the US. Great blog!
It’s a result of non-rhoticity in most of England. The spelled “r” in “erm” is not pronounced as such.
In most U.S. dialects it translates as “um.” Even in non-rhotic American dialects, “erm” is a sentence stopper on the written page.