The other day, I was hunting for a word to describe someone I know. The trait denoted by this word is the tendency to rapidly spot--as though unconsciously seeking out--double meanings, especially of the racier sort, in messages whose intent was probably innocuous.
I think such a person would often be called dirty-minded:
tending to have vulgar, obscene, or lewd thoughts, interpretations, etc.
(from Dictionary.com, based on the Random House Dictionary Unabridged)
Should you fail to find a common word that fits the bill you might want to consider Finbarresque.
Finbarr Saunders is a character in Viz comic-magazine http://viz.co.uk/category/finbarr-saunders/ noted for his ability to spot double-entendres in any conversation.
On the left, the Viz Finbarr Saunders. On the right, a different Finbarr Saunders from Knoxville, Tennessee; probably best not to confuse the two should you do an internet search.
His character is described in the Wikipedia page http://en.wikipedia.org/wiki/List_of_Viz_comic_strips#F_-_J as
a boy with a good ear for homophones. The strip almost always revolves around his liaisons with his neighbour, Mr Gimlet, whose manner of speech is always interpreted by Finbarr as graphically sexual in nature (in fact, it is deliberately scripted this way), usually when Gimlet is reminiscing about everyday situations with Saunder's mother. However, at the end of each strip, Mr Gimlet and Finbarr's mother invariably do end up having sex and make blatantly obvious verbal references to their doing so, but Finbarr interprets these as being nothing untoward. Finbarr's creator, Simon Thorp, described the character as a cross between a small boy and Sid Boggle (Sid James) from Carry On Camping.
A few examples from Finbarr's own comic strip.
Computer repair man talking to Finbarr's mother about turning on the computer. "Unless you know where it is you can be fiddling about for ages without getting anywhere but once you find it you just have to flick it with your finger to get the juice flowing"
Mr Gimlett tells Finbarr "I'm taking your mother on a tour of the north-west, first I'm going to Oldham, then I'm going to Bangor."
When talking of his wife's antique camera, a man says "I've spent many a hot afternoon with my face under her hood, flicking away at that button, trying to make those leathery old flaps to open up."
And some other examples of phrases used on TV/Radio which would be suitable material for Finbarr Saunders (note that this page has Finbar Saunders as it's sub-heading).
Pat Glenn, weightlifting commentator - "And this is Gregoriava from Bulgaria. I saw her snatch this morning and it was amazing!"
Harry Carpenter at the Oxford-Cambridge boat race 1977 - "Ah, isn't that nice. The wife of the Cambridge President is kissing the Cox of the Oxford crew."
Mike Hallett discussing missed snooker shots on Sky Sports: "Stephen Hendry jumps on Steve Davis's misses every chance he gets."
Ken Brown commentating on golfer Nick Faldo and his caddie Fanny Sunneson lining-up shots at the Scottish Open: "Some weeks Nick likes to use Fanny, other weeks he prefers to do it by himself."
While Finbarr Saunders may not be a terribly well-known comic strip character adding the -esque suffix to his forename is not without precedent.
2008 JOHN SAUNDERS UK Rivers Guide Book
[In response to a comment Bloody hell, what size beavers do you have around there???] - Forgot to add that with my surname all Finbarr-esque comments are naturally appreciated (+ old enough to have gone out with a girl from The Strawberry when Viz still referred to locals).
2015 DEJALU JustTheTalk.com
I'm sure I've told this story on here before, but I was in a meeting once with senior managers (and lowly me) and top boss, an American, decided to call another American colleague into the room for another opinion. "Let's all get Randy in here", she suggested. Cue me, convulsed with Finbarr-esque fnurks and snortles, while the rest of my colleagues (traitors!) looked on in pity.
Sadly, you probably won't find Finbarresque in a dictionary any time soon but you will find Finbarr Saunders in the OED.
The OED entry for fnarr fnarr was added in 2013 and the first citation for the use of fnarr fnarr is given to Finbarr Saunders (via Simon Thorp).
[OED] fnarr fnarr Representing lecherous or half-suppressed laughter. Freq. used to indicate sexual innuendo;
1987 S. THORP Finbarr Saunders Aug. in Viz: Big Pink Stiff One (1990) 115
‘It's a very big one, you see...’ ‘Fnar!’
I'm sure lots of people will have no idea what Finbarresque means, but then lots of people don't know what lots of words mean anyway; they'll just have to suck it up (fnarr fnarr).
Wikipedia contributors, "List of Viz comic strips," Wikipedia, The Free Encyclopedia, http://en.wikipedia.org/w/index.php?title=List_of_Viz_comic_strips&oldid=649839190 (accessed March 13, 2015).
Finbarr Saunders image (courtesy of Viz) from The Sydney Morning Herald - http://www.smh.com.au/sport/super-bowl-xlix-new-england-patriots-defeat-seattle-seahawks-2824-20150202-133jej.html
Finbarr Saunders image (courtesy of cityofknoxville.org) - http://www.cityofknoxville.org/citycouncil/members/fsaunders.asp
Finbarr examples taken from http://subbuteoz.hubpages.com/hub/Finbarr-Saunders
Other examples taken from http://www.visordown.com/forum/crap-jokes/finbar-saunders/281141.html
Finbarr-esque 2008 citation from UK Rivers Guide Book http://www.ukriversguidebook.co.uk/forum/viewtopic.php?p=343522
Finbarr-esque 2015 citation from JustTheTalk.com http://justthetalk.com/family/29930/are_they_still_being_unreasonable_/7229
If your acquaintance is quick with the old welleresque cliché “That’s what s/he said” you could call them the “Duke/Duchess of Wellerisms” or just welleresque, wellerian, or maybe even welleristic for short.
Granted, not all wellerisms are racy, but they all seem to involve double meanings.