These are the errors I'm getting. The installation went smoothly although some warnings were present. I don't think those warnings should produce the errors below.

Warning: chmod() [function.chmod]: No such file or directory in C:\inetpub\vhosts\something.com\httpdocs\gallery\zp-core\i.php on line 192

Warning: Cannot modify header information - headers already sent by (output started at C:\inetpub\vhosts\something.com\httpdocs\gallery\zp-core\functions-image.php:46) in C:\inetpub\vhosts\something.com\httpdocs\gallery\zp-core\functions-image.php on line 391

Any ideas as to what's the problem?

You did not tell us what version of Zenphoto this is which makes answering harder. Best guess is that cache folder created

It's for zenphoto 1.2.3. =)