Was I just sold a used cassette? I just bought this Shimano HG41 cassette and I noticed that not all of the teeth and dips between them look the same. You can easily see this in the image that I included if you compare the teeth on the largest sprocket on the left with those on the right. You will notice that those on the left are wider and the ones on the right are smaller. Also, the dips look like they have different shapes. I am wondering if that is how it is supposed to be, or if there was a manufacturing defect, or if I was sold a used cassette. For reference, I bought the cassette in-person and it came in the box (the box was a bit beat up) and instructions, although there was no plastic wrap over the cassette in the box even though there normally is (although I am not sure if they only do this for higher end cassettes).
In all likelihood, the cassette is new.  The cassette is manufactured this way. The difference in teeth shape and depth is to assist the chain take-up when you change gears.
Look for wear marks on the ramps and grime between the cogs - a new cassette should be clean with no marks.  While it could be possible to clean a used cassette to 'new' condition, (likely more expensive than a new cassette), it would be next to impossible to remove wear marks off the ramps.