I've had that happen, but the ads only show up in that one app. They can't install ads across my whole iPhone like most adware does.

May be the case on iOS but with Android I've had apps that stick extra shortcuts on my homescreen and spam notifications every few hours. This makes battery life and usability a lot worse throughout the phone until you can find and kill the offending app.

If that happens again, use one or more of these apps to find the offender:

Ad Network Detector

Addons Detector

AirPush Detector

With Android 4.1+ (4.0? can't remember) if you long-press on the notification it will tell you which application is responsible for it.

This is similar to saying "what stops a bad guy with a gun is a good guy with a gun". Alternatively, you could regulate, i.e., locking down the platform and sandboxing all third-party apps.

A better alternative would be for google not to publish this shit on their store but still allow useful background notifications and allow third party manual installation.

I want to switch to Android, but I fear needing to have constant vigilance over what I install. Like running a Windows install but forced to use Java as well.

However, it's still preferrable to Apple's draconian policies.

I've been running Android since 2.3, I've not installed a malicious app yet (to my knowledge of course).

If you want, you can install security tools which scan apps prior to being installed, like Lookout, which will alert you to various issues.

Yes there's a lot of spammy apps, but if you're even halfway aware of what you're doing, you'll have to be very unlucky to be caught out by one.