What is Malachi (or G-d through Malachi's mouth, or whatever) supposed to mean about tithing? Why did we have to pay full price to priests that offered impure sacrifices? Or am I missing the point?
I think you're confusing a few things.
The process is that the non-priest picks an animal for sacrifice, and brings it to the priests for them to process it.
In 1:6, G-d says:
I.e. the priests don't regard their duties very highly. Therefore ...
I.e. when the non-priests show up with these awful animals and say, "hey, priest, slaughter this as a sacrifice", you just roll your eyes and go, "good enough for the Temple, fine", instead of rejecting it and encouraging the people to do better.
(As explained by classical commentary Radak.)
So the priests aren't doing their jobs carefully enough, but they're still going through the motions. But it's the common people who are choosing to bring bad animals to begin with.
In 3:10, Malachi (quoting G-d) is reiterating the commandment (as transcribed by Moses) to give the tithes of produce to the proper people for their personal consumption (Levites or priests, as all priests are Levites too); that obligation hasn't changed. The commoner is supposed to do his obligation, and then the priests are supposed to do theirs.
Mind you, Malachi is a short book, but that doesn't mean it was all one long message. Different segments of the book were likely different prophecies, spread out over time.
Does that help?