Verified this on a clean install of drupal 6.20, ubercart 2.4, and multiprice 6.x-1.0 or 6.x-2.x-dev.

To reproduce:
- Install drupal 6.20
- Install ubercart 6.x-2.4 (only need to enable "product" and "store")
- Install multiprice 6.x-2.x-dev (or 6.x-1.0)

Add "region select" block to content of page.

Turn on normal page caching: Admin -> Site Configuration -> Performance -> Page Cache -> Caching mode: Normal

Logout of admin mode.

Change the drop down menu from one country to another (i.e. United States -> Canada). Then change back to the former country (i.e. Canada -> United States). The second time the country is changed, it will stick on that country until the cache is cleared or disabled.

It appears that the block or form is somehow being cached even though "block cache" is disabled by default and the module also specifies for it not to be cached.

I'm surprised no one else has experienced this issue since it has been reproduced on the most basic install and page caching is typically used in production sites.

Let me know if I can provide any further information!!