What should I look at to see what patches are installed on APM?
You can find the HIS files under:
\Program Files\CA\SharedComponents\APM Common Services\<servername>.his
\Inetpub\wwwroot\Unicenter Asset Portfolio Management\<servername>.his
\Program Files\CA\Unicenter Asset Portfolio Management\<servername>.his
However you can also look under Control Panel -> View installed updates
However they may not always show there and you may want to review the techdoc 000009550 titled "After applying any CA Asset Portfolio Management prerequisite, cumulative or test fix patch, the patch level is not displayed under Control Panel -> View installed updates"