Can the Moon really look full for several nights?

A full Moon is a phase, not a one-night switch. The lit portion changes gradually, so it can look almost full for several nights around the exact full phase. The shadows on the lunar surface also shift as the angle of sunlight changes, and the Moon’s changing position in the sky can make the view seem different from one evening to the next.

Brightness can vary too. The Moon may look more striking when the sky is clear and dark, or when your eyes have adjusted to the darkness. Haze and thin clouds can change its appearance as well. If you jot down the date, time, and general location, then compare those notes with a lunar calendar and a weather report, you can separate the phase from local viewing conditions.

Clouds are the part that’s most dependent on local conditions. Different weather patterns bring different mixes of high, thin clouds and lower, lumpier clouds, so a stretch without puffy-looking clouds can happen without anything unusual going on. What you see also depends on where you’re looking and at what time.

If you want to compare observations, note the time and check a local forecast or cloud observation for that period. One person’s view from one area won’t describe the whole sky.

I’d separate the observations rather than treating them as one pattern. For the Moon, check its phase on the dates you noticed it. For the shadows, compare views taken at similar times and with similar camera settings, since exposure can make the bright and dark areas look quite different. For clouds, record the type and coverage over several days.

A few impressions are easy to skew because our memory is better at holding onto striking nights than ordinary ones. A simple dated log or photos with consistent settings gives you something concrete to compare, without assuming the change is either remarkable or meaningless.