Media Companion looks for a couple of things when a movie is selected.
If a local trailer exists then the button shows "Play Trailer"
A local trailer is named like the movie +-trailer.ext
If a local trailer does not exist then MC checks the <trailer></trailer> tags within the nfo for a valid url, if one exists then the download button will be displayed.
It does seem that there is an issue with the change movie tab and the trailer link - looks like it is not saved and I will fix this for the next build.
For those who never see trailers, MC can only download a trailer from IMDB, and those parts of the world for which IMDB has trailers.
If you never see any trailer button using MC then have a look on the IMDB website, it may be that you live in a part of the world with no access to them.