I'm not a long-time forumer over here, not sure about the section. No one has moved it, so it's probably fine
3.5mm pitch is still pretty usable, so a good choice.
3mm radius empty around the middle of the screwhole is good, 3.5mm is better. Freedom from components is essential, traces are fine unless you screw in super hard and break the soldermask (it happens). For a low qty board like this, it probably won't matter. Also, everything here is super low voltage, so the penalty for failure is fairly low.
The Adafruit LCD is a random design from China,
Ruite Electronic specifically. I wouldn't be surprised if the design isn't great
Keep in mind that they are 2.8mm holes, made for an M2.5 screw, which will have a smaller head (as will the standoffs).
M3 hex standoffs come in a couple of varieties: SW5.5 and SW6. The latter is 6mm between *flats*, not 6mm diameter. I've attached an image showing this. Please excuse the very poor dimensioning tools in Altium.
Ignore the comment about the ICSP, it looks ok now.
Square vias: Eagle is weird.
Doesn't really matter what the value is, as long as you know how to scale the output - you won't be able to get all the way to 5V anymore.
Is the input bulk cap a
TH ceramic or an
AlElectrolytic?
Your SM decoupling cap (?C1) should be right at the pins for the micro, not an inch and a couple vias away. (Yes, either would probably work fine in this application, but it's a good practice to get into!)
If you rotated your tactile it'd route better.
You could get rid of half of the bottom side traces with a few changes. You'd then be able to slap down a ground plane on the bottom side, which'd be better.
ICSP p1 could be routed around the back of the one to its right, and then the 5V line could go straight down.
If you have a ground plane, then instead of routing ground you just pop down a via, which gets rid of the GND routing problem you presently have.
What's with the weird kink in the trace from P1 of the bottom left header?