That's normally not a serious problem. What car model and engine size do you have? Some valve covers have two bolts in the middle that can be tightened a little, and a reusable rubber gasket. Tightening those bolts half to one turn will stop most leaks. If gasket sealer was used, the old material must be scrubbed off and a new bead of sealer applied.
As for things that can go wrong, if old sealant is scrubbed off and allowed to fall down into the engine, it could plug an oil passage to the filter or it could plug the oil pickup screen. Those can lead to catastrophic engine failure. The leak itself will lead to oil loss over time, but usually at a rather slow rate. You'll want to check the oil level regularly. As long as the level is above the "Min." Mark on the dipstick, you don't need to add any.
No mechanic likes working on a slimy engine. If there's a real bad coating of oil all over the engine, there's always the risk of a fire, although that's pretty rare, but sometimes other electrical problems develop right after someone uses engine degreaser and power washes the engine. If time is not an issue, the best approach is to pressure-wash it, then let it sit a couple of days to dry off before attempting to start it.