Lol, had that happen in either Saints Row 1 or 2 (I think 2, but I played both around the same time.) Some chick got her head stuck in a metal diamond patterned gate. I would run into it and it would stretch out. Finally pushed it far back and it was stretched out like 10-12 feet in game.
As for me on The Third, nothing major. Random nitro boosts left on the street. Got some photos of them coming out of my guy's buttcheeks.
A rocket from the launcher left in my hand after I switched weapons. I messed around with this one for a bit just curious. Firing weapons (even the rocket) didn't fix it. Neither did changing/buying clothes/going naked. I finally saved and reloaded and it left.
Motorcycles front wheels sticking in the ground... mainly the Estrada. I think once with the Sandstorm.
Fully upgraded the Decker crib and fell through the top from an aircraft. Got stuck inside. Luckily it was right after a mission, so I reloaded.
Only one that's bothered me is the garage. I have a decent bit of vehicles in there and it likes to freeze/lock up. I pretty much just jack whatever I want now.
Oh, and one from co-op. He was redoing his character in Image As Designed, so I was out pissing off gangs. A luchador ended up stuck in place running. I took some photos and everytime I'd come out of the photo, he'd fly backward (like a split second moonwalk) maybe 5-10 feet, then rush forward and keep running in place. Finally killed him and walked toward the building. A minivan was stuck doing the samething, only a little less noticably due to the size ofthe vehicle and the distance being the same. Took photos and the same thing. I finally shot her in the face.