Minecraft – Graphical Bug In Minecraft

Sometimes even if it passed the minimum required configuration, you won't have a perfect gameplay. Some glitches like this may occur because of the small amount of RAM left to play the game and the graphic card can't handle it at all. Running Win7 on 1Gb of RAM .... seriously, you should consider putting more RAM since Win7 already needs that 1Gb of RAM to run in the background.

Win7 on 64 bit needs at least 2Gb of RAM minimum, so I think you should upgrade

http://windows.microsoft.com/en-CA/windows7/products/system-requirements

It looks to me that it isn't a bug that's causing the seeds to pop out, but your lack of lighting. If an area is too dark, seeds will pop out. I don't know why the other one pops out too, but you can at least try to increase the lighting. That should fix the problem.