(This is a slightly reworded repost of someone else's reply on this topic made on the discord)
imprecise UVs - due to how the older engines handled texture data1 the further your geo is from 0.0.0 in the map file, the more textures coords will be off. this is mostly apparent in trim sheet workflows. The fix on the Unreal side is to go into the static mesh and tick "Use Full Precision UVs".2
completely borked UVs - if HammUEr has to do guesswork triangulating a brush, this will potentially not only break the geo itself, but the UV data on it so more extreme distortions will be visible. triangulate all your meshes inside your .map editor prior to export to prevent this. this can also just be due to HammUEr forgetting3 that it needs to use valve 220 format texture coords for interpreting your map. checking and unchecking the box a few times can fix this
black faces - related to the problem above, triangulating usually will fix this, it's a result of broken normals. sometimes it wont, but using normal correction inside of the UE modeling tools can fix. if this doesn't resolve the issue, all you can do is either use volumetric lightmaps or author the mesh without HammUEr using .obj exports and clean up in your modeling suite
1: Contiguously, as far as I can figure out.
2: Note that this needs to be done on a mesh per mesh basis at the moment (or with a script). I will try to add this as a default option down the line.
3: I will... look into this.