The error message for the problem pictured above already gives u a hint. The fix is quite easy.
You only have to install/ update ur Installation of the Microsoft Visual C++runtime.
There are various versions around, not sure which Warband uses but if you install the most recent of the say last 4 versions u should be all set. I guess it might be 2005, so you should start from there and go all the way up to be save.
http://www.microsoft.com/downloads/en/details.aspx?FamilyID=200B2FD9-AE1A-4A14-984D-389C36F85647 (32 Bit)
http://www.microsoft.com/downloads/en/details.aspx?FamilyID=EB4EBE2D-33C0-4A47-9DD4-B9A6D7BD44DA (64 Bit)
Also keep in mind if u use a 32 Bit Windows or it's 64 Bit Edition (in the latter case it might be good to install both the 32 and the 64 Bit runtimes).
Somehow the patch increased chances of this happening (above pictured error messages), not sure how the details are, maybe somehow some scripts which haven't been used before, no idea really how that works but a friend of mine hadn't installed up to date Visual C++ runtimes, but could play perfectly fine before anyhow till the new patch came out, so I instructed him to install like the last 3 or 4 Versions and afterwards it all went back working as it should.
For the other issues, freezes and slowdowns, really some details on ur guys systems would be needed to look any further into it, otherwise it could be caused by quite a lot, (outdated drivers, overheating, buggy drivers which randomly changes power states while u play, power management features, /USERVA and so on)
One more thing, alt+tab or the steam overlay (with chat windows, or webbrowser running or nothing at all just sitting there but switching back an forth) doesn't do well with Nvidia cards/ drivers for some reason up to the latest nvidia driver I for one can reproduce a lot of issues and crash or get visual artifacts which look like ur card is overheating/ failing, if I alt-tab or use the steam overlay in the wrong moment, - mostly map changes/ loading screens.
On ATI cards I know of problems if the option "load textures on demand" is not set, which might have been solved with newer drivers.
One more detail, Warband, even tho it clearly is no "Crysis" with it's Engine (tho it isn't as bad as some ppl make out it's visuals to be) is quite heavy on the RAM usage, on my System it easily eats up around 1 GB of System RAM (whereas the video cards RAM, I got 1 GB doesn't seem to influence anything in the game) right after I started the game (cRPG module) and am just sitting in the menu, on some maps it can easily end up at around of 1,5 GB RAM (which already can be a cause of problems for 32 Bit Windows Editions), while it still isn't that much nowadays if you think of 3-8 GB of System RAM it can strain some systems quite a lot, somehow the way the engine/ game mechanics handle stuff doesn't seem to be that effective/ optimized. Would be interesting to see if that has changed at all in it's newest incarnation (With fire and sword).