Those tiny black dots always appear during the crossfade/transitions section after a couple of crossfade use. They are only gone when I close and open the software again. I never had this problem with Vegas 7 compared to 10.
Is it because of the low memory ram (2gb), weak 3d card or something else?
Vegas 7 doesn't have GPU acceleration and Vegas Pro 10 is the first version that does so your graphics card now plays a significant role in editing.
Try turning off GPU Acceleration by setting it to None under Options | Preferences | Video and see if that fixes the problem. That will either confirm or eliminate the graphics card as the cause.
Also make sure that you are using the latest build of Vegas Pro 10e Build 737/738. You may be chasing a bug that has already been fixed.
BTW, 2GB of RAM is absolutely too little for video editing but is probably not your problem. You would see red frames if you were running out of resources/memory.
That option to select GPU acceleration of video processing on the Video tab appears to have shown up in Vegas Pro 11. In Vegas Pro 10, there is an Encode Mode switch in the Render As tab where you can select whether to use GPU for rendering.