There's not too many signs that alert you to a bad oil filter and you should change the engines oil filter along with the engine oil every 3,000 to 5,000 miles to prevent problems.
When an oil filter goes bad though and gets clogged it causes debris that would otherwise get filtered by the oil filter to make its way to the engine and bearings in the engine which can lead to engine damage and a possible seized engine.
Your engine oil pressure might even rise or get too low as a result of a clogged oil filter and if in doubt and it's been more than 5,000 miles since you changed your oil or oil filter you should change both the oil and oil filter.
If you have an oil pressure light or oil light or a change engine oil light in your vehicle then it may come on alerting you to needing an oil change and oil filter change.
When you change the oil filter you should always drain and change the oil as well.
Oil is the lifeblood of the engine and if you do not change the engine oil and oil filter often enough then your engine can be damaged.