UV mapping going wrong

Hello everyone!
I am running into some strange problem here!
The textures displayed in the Editor are not shown correctly:
(left side shows UV mapping in Blender, right side shows rendered texture in Unity)

Does anybody have a clue what I might be doing wrong?
I did the same procedure on another object and it worked perfectly, but this time not so much!

Many thanks for any hints,
Greetings,
Shu

The texture in blender is point sampled, and if I was to guess is a non power of 2 texture. The one in the editor is bilinearly sampled.

Thanks for your reply, but if you are talking about “Filter Mode” of the texture, I already set this to “Point (no filter)”.
Also, the material is rather simple. Here are screenshots of the settings I use:
2525735--175213--image2.jpg

2525735--175214--image3.jpg

Oh and the texture is 128p, 128p, RGBA, .psd, so nothing fancy.

EDIT:
I somewhat made the problem less bad (for whatever reason, setting the original file’s resolution size to 512p got rid of the blur and scaling the UVs to .95 made some of the fragments go away), but there is still weird stuff going on:
2525735--175215--image5.jpg