World flashes and disappears -- rendering issues and bugs

This glitch only happens on a server that I play on, which is personal. I run the server on my mac (Mountain Lion OSX 10.8.4) and play with family. My co-players do not receive this glitch, but at first they were experiencing certain symptoms.

The glitch itself is nonstop and seems to have something to do with chunk loading and the amount of ram dedicated to minecraft. With 1GB allocated the glitch is prominent and very hindering to gameplay. The terrain flashes on and off, as if the render distance is changing from 2-14.

With 2GB (whilst the server is running on the same computer) the glitch is less prominent but I'm unable to use that much because the server begins to lag (I can only take so much ram with each program). So I compensate and do 1.5GB and it works pretty well. I still see flashes when the game gets more memory-intensive. I'm not completely bothered by this, but it is definitely annoying.

My suggestion is to take a look at the rendering setup of minecraft. I'm sure it doesn't have much to do with the fact that I'm on a mac. I've never had this problem before. And before I had set the allocated RAM lower, friends and family were having glitches like doors opening but not allowing entry, chests opening but containing nothing, trying to plant seeds but nothing happening.

This is probably due to the allocation of memory, but minecraft should not flash just because I have low memory. Lowering render distance does not help, and settings are on lowest of low in an attempt to fix it.

See Screenshots below

After trying to take screenshots of the occurrence, I discovered another glitch within this glitch.

The first image is a good representation of what happens. The render settings are on high, and it also hid parts of the GUI. I say parts because the chat is still visible.

The Fix:

If you visit the website https://db.tt/K4ryhoIt you will find a dropbox download of MCPatcher 4.1.3. As of Dec 18 2013 this is the most recent working version with Minecraft 1.7.4. MCPatcher, if you wish it to, provides support for HD Resource packs and customization beyond that of normal resource packs. However, if you don't care about that then it's all the same by deselecting "Allow HD" and simply clicking the patch button. This will (it has worked for three people that I know had the issue) fix the bug completely and even run minecraft slightly faster, although you won't really notice. Please post in the comments if this does not fix it.

Note to Moderators of the site: Running a simulated crash, I compared my friend's log to mine and there were no differences. I had the bug, the other didn't. I'm not sure why this is, but I figured it would be pointless to post a log that was completely normal.