I replaced the seal between the catalyic converter and the pipe in front of it. I was able to move that pipe from side to side like it had some kind of joint in it. Is this normal?

Had detachment between muffler at the muffler body and the after-cat pipe. Sway bar was hitting it which caused metal fatigue. $40 fix at local (honest) garage. Movement just seemed to happen suddenly... but all exhaust system bits have to be correctly welded.

That doesn't sound normal. You could have a loose nut at the header to exhaust manifold connection, or the welds on the header pipe may be failing, or the mount to the bellhousing may have come loose or rusted apart. In any case the header pipe and the exhaust manifold should be pretty firmly connected to the engine and the bellhousing, and to each other. Maybe you'll have to get further under there with a flashlight to trace down the play in the system.

Tom
'86 245DL with recent header and catalytic converter replacements