This sound like a real bug in the app and of course it should be fixed. However it can be hard to find since it is not easy to reproduce. Thanks for the thorough info though.
Chess.com mobile weird behaviour

I just had this happen again -- this time I scrolled down to the "Back" optioninstead of up, so that's not it, but on both occasions I've very clearly seen the piece jump to its new position when the "Back" option is selected just before the screen changes to the main page.
A pawn again, this time one of mine from c4 to b5.
Although I still can't consistently reproduce this, I hope the additional info helps in it's diagnosis and ultimate resolution as I'm currently a little leery of the accuracy of the positions presented as a result of this bug.

to OrionBR - I am curious to know how you managed to take screen shots from your mobile and get them posted here?

@rdallison:
http://www.antonypranata.com/screenshot/screenshot-symbian-os
That works for Symbion S60 3rd edition mobiles( Nokia N95 in my case )
Google with your mobile model for 'screenshot' app.
After reporting a minor issue I have another major issue to report in Chess.com mobile ( I am not if this forum is the right place. If not, please let me know the right place for reporting bugs )
Following is the issue:
Since I couldn't understand what exactly happened in previous moves, I planned to play it over the computer and clicked "Back"
The a1 Rook jumped to the b8 square :)
Repoducible: No. I am not seeing the same issue in any new game as of now.
Workaround: Refresh your games.
I think this should be fixed to avoid any confution.