My 1991 Honda Accord is dropping oil onto the hot cover in the front. Also, the service engine light soon comes on after driving about 10 to 15 minutes. What possibly can be wrong? I think the cover gaskets may be bad.

If oil is coming out from the bottom of the your valve cover, the gasket is bad and should be replaced, but that probably would not cause your check engine light to come on. The oil dropping down on what I take to be your manifold cover may be getting into you O2 sensor somehow and causing that to send an error code to your computer. Replace the gasket and see if that stops the code. If you want to clear the codes, pull the radio/backup fuse from your underhood box and keep it out for more than 10 seconds (with the car NOT running), then put it back. That will clear your computer. If, when you replace the gasket, the code comes back, I would have it checked by someone who can read the codes on a Honda that won't take a DTL code reader (you have to jump the little DTL that you have and read the flashes of the check engine light that results; long flashes and short flashes, then find a chart to see what they mean; a bit involved). If oil is coming out from the bottom of the your valve cover, the gasket is bad and should be replaced, but that probably would not cause your check engine light to come on. The oil dropping down on what I take to be your manifold cover may be getting into you O2 sensor somehow and causing that to send an error code to your computer. Replace the gasket and see if that stops the code. If you want to clear the codes, pull the radio/backup fuse from your underhood box and keep it out for more than 10 seconds (with the car NOT running), then put it back. That will clear your computer. If, when you replace the gasket, the code comes back, I would have it checked by someone who can read the codes on a Honda that won't take a DTL code reader (you have to jump the little DTL that you have and read the flashes of the check engine light that results; long flashes and short flashes, then find a chart to see what they mean; a bit involved).