Okay, I think I've tracked this one down. It isn't a problem with your iPod or iPad, it's a problem with the router itself. Its DNS has been overwritten so that it randomly (about 5% of the time) will redirect you to one of their sites.
Because you're using someone else's open access point, there really isn't anything that you can do about it except to stop using that particular router.
For more info, see these pages:
As for the first paragraph: Yes, the OS version can be changed (at your own risk) by opening said file (/System/Library/CoreServices/SystemVersion.plist) with a plist editor of your choice and then changing the version from 5.1 to 6.0.1 or whatever you intend.
The device type can’t – and even if it could, shouldn’t – be changed, though, as there are versions for each and every device and while the OS version might change over time, the device itself obviously won’t automagically transform into another device. There is a file called after the device you’re using in many of the subfolders of /CoreServices/, though. In case of an iPod touch 4th gen, the name would be N81ap.plist. In there, you find the capabilities of the device.
EDIT:
I just spoke with a friend of mine. He told me that yes, you could modify the version. But you would also have to change the ProductBuildVersion – for example from 9B208 (iOS 5.1.1) to 10A523 (iOS 6.0.1). But this, of course, might lead to failure because the app might try to use methods not available in the OS version you pretend to be using.
By copying the values of (for example) N81ap.plist to #yourDevice.plist, your device (theoratically) gets the features of n81.ap. This could also lead to failure, because Springboard (or others) might need functions not available to the device you are actually using.
For some apps, it is quite easy to set the required phone/device, though. In that case you would have to search for a value like “requires telephony” or alike.
Best Answer
I hate to say it, but in all my years of jailbreaking I have yet to see any type of malware have any real impact on the iOS community. Sure there was the infamous SSH vulnerability, but that was patched rather quick. That's the beauty of jailbreaking; we don't have to wait for Apple to release a fix. Most people fear that jailbreaking is insecure and puts your device at risk. That's far from the truth. My favorite example is the jailbreakme.com PDF exploit for iOS 4.3.3. At the same time they released the exploit, they pushed a patch to Cydia. As soon as you jailbroke, you were advised to install the patch, so that your device could not be further compromised. It took Apple a lot longer to implement and roll out their fix. In that situation, it was better to jailbreak than to not, because unless you had the patch, someone with bad intentions could have abused the exploit and done anything they wished with your device. Sure, you can be careless and install some malicious software, but most of the time it's the user's fault, because you always should be careful with what you do in a limited-regulation environment. As a final answer to your question, there were a few PDF exploits that were triggered merely be visiting a website (jailbreakme.com), but those vulnerabilities were never used for evil.
Edit: Another malware example has popped up, but it's not specific to jailbroken devices; it can remotely jailbreak any device without user interaction. This is the first time we've seen a remote jailbreak being used in the wild for malicious use. Apple has already patched it - they patched it quick. But the jailbreak community took a few months to patch it.