Changing spark plugs and one well was full of oil. I took off the valve cover to replace the gasket and noticed that there was quite a bit of oil puddled in the cylinder head. Is this normal or could there be more problems?
2002 Hyundai Elantra
If you are suggesting there was oil inside the head where the valves/cam(s) are located, this would be perfectly normal. If you are saying the oil puddles are outside of the valve/cam area, this isn't normal, but should be taken care of by you putting a new valve cover gasket on the engine. I would say, clean up the entire work area, complete the replacement of the valve cover gasket, then monitor for leakage. I'll bet you'll be fine.
There should never be oil on the plug, neither on the "inside part" nor the "outside part". If oil is on the "inside part" of the plug, then the problem is likely a head gasket, valve stem seals, or worn rings. If oil is on the "outside part" then the problem is likely the valve cover gasket, which you mention that you have replaced.
Oil under the valve cover, on the head, is normal. It is the drain oil that had be squirted on the valve train. During engine operation, excess oil from this area drains back into the crackcase via drain holes. If you suspect that there is excessive pooling in this area then check that the drain holes are not cleared.
Note that plugged drain holes, and thus excessive pooling, may contribute to excessive oil to make it past the valve stem seals, thus polluting the plugs.
The cylinder head on an engine gets very hot. The seals on the cam cover gasket and spark plug tubes can and do deteriorate and leak onto the cylinder head exterior. One other point to watch for is the hoses for the PCV valve. If they have gone 'soggy' or otherwise blocked they will leak oil onto the head. A blocked PCV hose will also cause oil leaks on the engine where-ever it has seals due to internal crank pressures.