MellonC00

A new guy at the shop I usually go to left the air filter housing hinges open and left about 1 inch gap. I found this about 100 miles later and corrected the issue. But here is what I found out if your air filter is, well, just open like the situation I had.
1) there is more noise under full throttle. the noise is mostly exhaust noise. seems as if I put in a new cold air intake or something.
2) there "seems to be" more power. but my butt dyno isn't accurate.
3) my mpg dropped by about 7 to 10% in that time driving the same route. what is funny is that the computer must have done something to the fuel mixture because the mpg didn't come back to normal until well after I closed the air filter housing and everything was back to normal. I think it took another 100 miles after I rectified the problem.

riredale

I'd expect more horsepower only if the filter was full of dirt. I wouldn't expect any change in mileage because the computer would adjust the fuel flow to match the airflow.

Clutchless

It would have inhaled warmer air from the engine compartment which means less power as opposed to the colder air sucked in thru the filter housing intake which is probably in the front grill somewhere or pointing down somewhere to get cold air. However that may have been balanced by the extra air inhaled because the filter was somewhat bypassed.