Via Charlie Pierce, I found the story of Seth Moulton, running for the Massachusetts 6th District seat in the US House of Representatives. Apparently, instead of exaggerating his record, he declined to mention his Bronze Star and other decorations. (Here's another story.)
Is that even allowed?
UPDATE: It does occur to me that the last major politician I know of who did this sort of thing was George McGovern, who flew 35 missions over Nazi-occupied Europe and won the Distinguished Flying Cross. Make of that what you will.