If you mean can discs go bad with use then this part of the question is clear.

Yes if the media gets damaged in some way then it will go bad. Obviously the more a disc is handled the greater the risk. Error correction can often recover for damaged areas so you can make another copy but when all else fails you sometimes can retrieve most of the data by using bios level hardware access that bypasses windows safeguards. There are programs specifically written to do this.

This part generated some confusion because some weren't sure if you meant... Do successive generation copies of a dvd degrade more with each copy?

That would imply that generation 1 is good, generation 2 is still good but now has some errors. Generation 3 is like 2 but now has new errors.
That would make no sense. Either copy 2 is good or it is not. It cannot posess errors and be good. It can have areas that require error correction to kick in because the disc has a physical or burn flaw and is hard to read but if you make another copy and are successfull it will not pass on the reading flaw. Let's not get confused with a burn that is good but somehow through deterioration of the physical disc, dirt, scratches, exposure to heat, warping etc... suddenly cannot be read or . There is error correction on each disc and if data can't be read then error correction will be attempted. That is not because it was stored bad but because it had a problem being read.
Lets say I have a read error on generation 3 and lets say that error correction works when I am making a copy of generation 3 to generation 4. Generation 4 is good because the same physical flaw that caused the error and difficulty reading on 3 is not on generation 4. Generation 4 is good and the data is the same but the physical disc itself is easier to read so to you it is better not worse than 3 but it's also the same as generation 1 and 2. In the language of 1's and 0's (or pits, reflectance and prepits) the data from disc 1 to disc 4 is identical.

Unless I am using a blind read and write with no error checking I can't pass on errors to the next disc. But some will argue I have bad video frames isn't that bad data. No. Digital writing passes whatever crap you feed it. If I copy garbled video that won't play from my hdd to a dvd disc it will be written just as it was on my hdd and still will be garbage but an exact copy. There is a possibility of data corruption being introduced by a badly written burning program. lets say the burning app looks at a character on the source disc and somehow passes a different character to the target disc then that data corruption is introduced by a bad program but not by deterioration of the data. An application like that won't last long.
So will a disc get worse from generation to generation? I can't see how that's possible unless you deliberately bypass error correction and create errors between copies.