My worst experience was with a meat market in the town where I grew up. They had a small oil drum smoker out back, and kept a pot of chopped beef in sauce going up front. Not the sort of thing you'd dream of as barbecue, but if you were in there to get some meat anyway, the occasional sandwich wasn't that bad.
Until the time after I'd moved away and was back visiting family there and made a trip to that butcher shop we'd used for many years. I picked up a bag of their sandwiches for lunch. When I opened mine to add a shot of Tabasco, it was crawling with maggots.
The worst thing was that, when I took the bag full of maggoty sandwiches back, they didn't seem all that surprised. That was my last trip there.
A distant second place goes to what may have been the most heavily-advertised barbecue joint anywhere: Ward's BBQ, Shepherd, TX. All roads leading in its general direction were plastered with loads of signs advertising it, as well as what they called cider. The general advertising approach was sort of Burma-Shave on steroids, counting down the miles to go.
Needless to say, the meat was pretty grim and greasy, served on a pile of white bread, and the cider - in a choice of flavors - was a lot closer to Kool-Aid than to real cider. The place's only reason for its continued existence was that it was in the middle of nowhere. Hopefully it's long gone by now.