How to properly play 720p/1080p media with subtitles through MHL (HDMI out)? I own a Galaxy Note and got a MHL cable for watching movies on my Sony Bravia.

I'm having some problems for playing it nicelly.

With hardware decoding:

Only the stock samsung "Video Player" is able to play at TV resolution with the subtitles. The problem is that it seems to have an annoying bug that makes the subtitles stuck. After someone ends talking, the last sub don't vanish/disappear, it keeps there on the screen until the next speech. It's discussed at an old xda thread but no one was able to provide solution at that time.

With Software decoding:

I can get the subs with a third party player (like MX Player), but it doesn't stream the video to the TV directly, like the stock video player does. What I get is a rescaled screen, like when not playing a video, just browsing Android, and as such, not only it's not playing 720p/1080p video, but also, I get black areas because the phone aspect ratio doesn't match the TV aspect ratio.

Is there a solution for this?

As can be seen in the mentioned thread, there was a "stuck subtitle" problem with another Samsung device. Is this a bug with all Samsung devices?

Is there an alternative player that can play videos with hardware decoding and also display subtitles? So it can take all my TV screen.

I've checked this thread too, but there was general misleaded advices...
If you're rooted you could try to force a certain combination of phone screen resolution and DPI using Second Screen and maybe your selected video player will conform to that even as the video is being streamed out through MHL.

Just make sure you keep failsafe options like "don't keep settings after restart" enabled in case your experimental Second Screen settings make your screen unusable.