Keep the system software up to date is all you really need to do. The malware to which you refer had nothing to do with Adobe's Flashplayer.
Helpful Links Regarding Malware Protection
An excellent link to read is Tom Reed's Mac Malware Guide.
Also, visit The XLab FAQs and read Detecting and avoiding malware and spyware.
See these Apple articles:
Mac OS X Snow Leopard and malware detection
OS X Lion- Protect your Mac from malware
OS X Mountain Lion- Protect your Mac from malware
About file quarantine in OS X
If you require anti-virus protection I recommend using ClamXav.
You should upgrade OS X to the latest version, 10.8.3, provided your computer is able to run Mountain Lion:
Upgrading to Mountain Lion
To upgrade to Mountain Lion you must have Snow Leopard 10.6.8 or Lion installed. Purchase and download Mountain Lion from the App Store. Sign in using your Apple ID. Mountain Lion is $19.99 plus tax. The file is quite large, over 4 GBs, so allow some time to download. It would be preferable to use Ethernet because it is nearly four times faster than wireless.
OS X Mountain Lion - System Requirements
Macs that can be upgraded to OS X Mountain Lion
1. iMac (Mid 2007 or newer) - Model Identifier 7,1 or later
2. MacBook (Late 2008 Aluminum, or Early 2009 or newer) - Model Identifier 5,1 or later
3. MacBook Pro (Mid/Late 2007 or newer) - Model Identifier 3,1 or later
4. MacBook Air (Late 2008 or newer) - Model Identifier 2,1 or later
5. Mac mini (Early 2009 or newer) - Model Identifier 3,1 or later
6. Mac Pro (Early 2008 or newer) - Model Identifier 3,1 or later
7. Xserve (Early 2009) - Model Identifier 3,1 or later
To find the model identifier open System Profiler in the Utilities folder. It's displayed in the panel on the right.
Are my applications compatible?
See App Compatibility Table - RoaringApps.
For a complete How-To introduction from Apple see Upgrade to OS X Mountain Lion.