#1: Properly sizing the image may have an affect. Has Tumblr fixed the whole “our default is edge-to-edge images on posts but we resize them anyway and it all looks like trash” issue? I have no idea. I have a script plug-in that make it so there’s still white bars on things. (Stylish + “Fix New Tumblr Photo Widths”). SO I still use the 500 pixel width for full-sized gifs, 245 for two-ups, 160 for three.
Anyway, never ever ever ever let Tumblr upsize your gifs because it looks terrible. So like, don’t do a one-row 400 pixel gif because it’ll be stretched to 500, etc.
#2: Sharpening. There are different tutorials to follow based upon what version of Photoshop you are using and what it is capable of. Back when I used CS5, I had to use a script. This is the tutorial I followed. If, however, you have a version of PS with the Timeline window, you’re in for a way easier time.
Mini tutorial under the break because of pictures: