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Since the S3 patch, I haven't been able to see gains in LP on the postgame screen. The numbers are getting updated correctly, it just tells me that it is loading data or something. It directly overlays 'Normal' if you have played a normal game.
There is also some discrepancy that I noticed between the LP in your profile page and the actual LP in the League's page. When viewing other people's profiles, everyone has 'Games Won: 0' with the 3 most played champions, as opposed to 'Games Played: X'
The 'See more stats' in the Leagues page just overlays on top of the page, without having a solid background, which looks very awkward.
When I got promoted in a division, it told me I got promoted to the same level division, when it actually properly promoted me in the Leagues page.
Basically I think all the underlying code is working, but the interface has a ton of bugs with it.
EDIT: When viewing an unranked profile, when you go to Leagues -> View Challenger Tier, the two More About the League System links are visible almost on top of each other.
EDIT2: Some of the emblems are being drawn with the wrong image.