You're not packing correctly. It sounds like you aren't packing the materials, because that's what the purple and black checkerboards represent. If these are models, make sure that in addition to the model file, you pack the texture. If it's just textures, you're doing the whole thing wrong.
You can also try
PackBSP, which is essentially the same but I find it a bit easier. Some people have problems packing specific content, though, and maybe 1% of people can't make it start at all.
An easy way to check how other players will see your map is to rename your tf folder to tf_old, then launch TF2 and load your map. TF2 generates the tf/ folder from scratch so anything not in your map will be broken. After you're done just delete the new tf and rename the old one.