If the file works fine in 3ds Max, and even in another program, Photoshop in this case, then obviously you can know that it was exported correctly.
If Milkshape can't load it properly, then Milkshape can't load 3ds Max files properly, that's all there is to it.
This isn't surprising either - .3ds is about the least portable 3D model format in existence. It's 100% propriety, and I don't think anyone ever bothered to really reverse engineer it (there are some libraries that can load .3ds, but it's always partial support at best).
Indeed, why reverse engineer something like this that keeps changing on an yearly basis, when 3ds Max can export to a huge array of other formats that are actually documented?
You can use
NeoDex, like Idaero suggested.
If you really must use Milkshape for some reason, then don't export as .3ds, but rather something else that Milkshape fully supports. Haven't used it in years, so I have no clue what that is.