Q:

Object in texture mode looks like solid mode

When I am in texture mode one of my objects looks like it is in solid mode. The model is textured like all other models in the scene, but it doesn't look like it is in texture mode.
Screenshot will explain better:
 

What this model looks like.
What all models should look like in texture mode.

A:

Ensure that Maximum draw type is set to Textured in Properties > Object > Display:

See this answer for a 2.8 screenshot.

