iPhone can have closed caption movie.

There has capability in iPhone and iPod touch but Apple never give any information on this to anyone. Here is websites.

iTunes Adds Closed Captions by Social Edge
Tutorial of how to make a closed caption by Israel Melendez, Jr.
[Updated: SUCCESS!] Non-Handbrake solution for Subs/Captions by Kneeslasher
Discussion about closed caption in iPhone in Handbrake forum