Hey guys, I was having this problem all along as well.
I doubt its the amount of ram or the cd reader that is causing this issue.
I have windows XP the game was working fine, before I re-installed the whole computer.
After that I naturally wanted to play Arma 2 again, but I was getting the same problem as you guys have, this CRC does not match error.
I extracted the files to my desktop at first using a out dated winrar (2002 version) thats when I first got this error when trying to install at around 60% completion and said CRC error in the language.pbo, after a while I assumed it may be the winrar's fault, so I got a newer version of winrar up to date and did the whole process again, the error came again but this time it was not the language.pbo file but misc2.pbo.
So something had happened when I gotten a newer version of the winrar.
I then tried opening it with 7-zip to extract the files. This however could not even open the Arma 2.mdf file.
I then remembered previous programs I had installed before I re-installed the computer, programs like daemon tools and magic iso.
Now I did not use daemon tools, but when I extracted the files using magic iso, the installation went perfectly without any errors, no CRC anymore.
I think that it has something to do with the files, that are being placed to the desktop or any folder.
If you have downloaded the game from steam and getting this error try extracting or moving the files with Magic Iso, if you have it on a CD, I would suggest to move the files using magic Iso to the desktop and then installing it. It worked for me, I hope this is the general problem, please give me feed back if it has worked for you. Cheers.