I have a 2001 z28 6spd w/ 65k miles. It just recently started to shake and a slight dull bumping sound which only can be heard from inside.... really you don't hear anything just feel it. It has a rough kinda choppy idle. Cam heads all stock. It's only at idle that it seems weird, it drives fine once going. When you shut the car off, it has one bigger shake. Sometimes when under slight bog in 5th I will get a misfire light for #5 cylinder. I cleared it and it hasn't came on since but shaking at idle won't go away. Could it be a broken motor mount.. my shifter does seem to move around alot, bearing in the bottom going, blown cylinder.... where should I start what should I look for? I do hear an exhaust leak, could it make it that far off that it messed with tuning? I have a scanmaster if any data off that will help.

 

Start by changing the plugs. If that doesn't take care of it, do a compression test; that will tell you the condition of the rings and valves.

 

check your valve springs. I have had some break 3 different times. You have a six speed so it is more likely to happen. Good luck.
PS the first time I didn't know and the valve dropped on the way to the shop, instant 4 grand.