He was a huge influence on a lot of British bands, most importantly (for me) Van Morrison and Georgie Fame. Songs like "Parchman Farm" and "Your Mind is On Vacation (But Your Mouth Is Working Overtime" -- simply iconic.
The NY Times obituary said that his songs were covered by (among others) the Kinks, though I can't recall any Kinks covers of Mose Allison tunes, at any rate on their studio albums. Can any of you think of one? I'd be happy to know if they did cover some Mose stuff.