If its for your car it will leak oil faster and therefore make you change your oil more often.
Neither your oil filter, or the fill cap need to be loose, the filter should be screwed on as tight as you can get it by hand only, and the fill cap should fit snugly so it does not come off. If the oil filter is loose or too tight you can blow out the seal which will cause you lose all your oil.
Place a drip pan below of the oil filter. Attach an oil filter wrench to the filter. Turn the wrench to the left. When the oil filter is loose turn with your hand until it comes off.
That would depend on how long the oil filter has been in use. At worst, the filter could become clogged and restrict or prevent the flow of oil through the engine.
A loose, improperly aligned or worn-out oil filter are common causes of car oil leaks. A loose or improperly threaded drain plug could also cause an oil leak to occur.
Possible, but more likely a leaking oil filter or valve cover
Nothing terrible will happen but the old oil in the filter will mix with the new. I would recommend you change the oil and oil filter again. This will insure that you will have clean oil throughout the motor.
You don't say where it is leaking oil from. Kind of hard to offer suggestions on how to repair. Could be oil pan cracked or loose, oil pan gasket, oil filter gasket, oil filter loose or cracked; valve cover gasket, etc. Is it smoking? Please give more detail.
Try tightening or replacing the oil filter it may be loose or the gasket may be defective
Somebody didn't install it properly and it vibrated loose.
The bypass valve will open and the dirty oil will bypass the filter and go throughout the engine. This will never happen if you change your oil every 5,000 miles and also change the filter.
Oil filter installed incorrectly as in too tight, too loose, the gasket was not oiled prior to installation, or the old filter gasket was left on. It can also be a valve cover gasket leaking and running down by the filter. Replace the oil filter and oil the gasket and tighten 3/4 turn after it makes contact with the mounting surface. If the leak persists if is not the filter.
You don't say where it is leakong from, but if from under the engine, it could be a loose or damaged oil filter, loose or bad oil pan gasket; damaged oil pan, loose plug on oil pan, bad main seal, cracke or broken block, just to name some possible causes.