Maybe everyone knows these already, but I'll just add some search tips, since some of this is about searching.

1. You can use - (minus) as Not.
A couple examples:
https://sakuga.yshi.org/post?tags=-presumed+-artist_unknown
https://sakuga.yshi.org/post?tags=impact_frames+-animated

2. Default search mode is intersection, but you can change to union by prepending ~ (tilde), e.g.
https://sakuga.yshi.org/post?tags=~metropolis+~giant_robo
or, both modes at once
https://sakuga.yshi.org/post?tags=~sports+~dancing+shinya_ohira

3. For searching by score and other numerical things, you can use comparison operators, like <, >, <=, >=.
Example:
https://sakuga.yshi.org/post?tags=score%3A%3C10+width%3A%3E%3D1000+animated

Surprisingly, this also seems to work with dates, e.g.
https://sakuga.yshi.org/post?tags=date%3A%3C2014-01-01

However, trying to search for something like "score:>10 score:<15", expecting intersection, i.e. all posts with score in range (10, 15), doesn't work as expected... I think it ignores the first one.

Also, for something like "~width:1500 ~width:1000", expecting union, i.e. all posts of width 1500 or 1000, again doesn't work as expected.