So here's a step by step guide for those who are faced with the problems (freezes player, the long pauses when switching tracks, etc.) after updating to firmware 1.10.
Video - http://www.youtube.com/watch?v=40Fx08jaqF4&feature=youtu.be
1. Copy somewhere, all your songs, movies, etc. from the player's memory
(because all data will be erased.)
2. Navigate to Settings - Backup & reset and press Factory data reset.
3. Wait until the player is loaded.
4. Now you can update the Sony Media Player and install your additional applications (Mx Player, Angry Birds, Skype etc ...).
5. Hooray
, now everything works fine without a pause, etc.
p.s. contacted Sony tech support three times - they could not help me. A bad Support
.