Well, first you can discount all shadow doubling caused by bad dies/planchets, you can discount all the ripple and ridge lines caused by striking pressure and die wear, you can discount all forms of split plating, and you can discount most of the clash marks you will find. All of this stuff is exceedingly common for 1980s cents.
Having said that, there are a number of pleasant surprises in the decade..
1980
DDO1982 LDC
DDO1982 SDZ
DDR1983
DDO (five different ones)
1983
DDR (one major, one less najor)
1983D RPM (pretty minor)
1984
DDO (doubled ear, then the one with doubling in the lettering)
1984D
DDO (nice one, often overlooked)
1985
DDO (little known, kind of minor)
1985D-1989D RPMs (a lot of them are nice, all of them are scarce)
1987
DDO (decent, but not major)
1988
DDO (a couple of semi-decent ones)
1989
DDO (a number of 'fat date' dies)
1989D
DDR (a few minor ones)
This is just the better stuff to look for...but you never know what you might find, so check everything. Problem with most people when they are just getting started is that they miss the fact that no book contains all that's out there, and even if one did, it should be used after you find something for identification - not to form a list of what to look through. Doing the latter will have you missing the chance to discover something new.
As for errors - the die and strike errors would be the same as for any other
Lincoln Cent (mostly any coin for that matter) - the planchet errors are what would be different. Unplated cents are more abundant (although scarce) for this period. A number of other minor oddities show up especially during the mid-1980s because of the composition change, but many of them are rather common and are collectible only for curiosity sake.
This is about as good as I can do from memory.