how to check if keylogger has been installed on iphone 4?

A keylogger or spyware, while not impossible, is unlikely. Most likely it's just a corrupted file in the iPhone's operating system. Try the usual steps: restart, reset, restore.

http://support.apple.com/kb/HT1430

http://support.apple.com/kb/HT1414

If you try restoring from a backup and that doesn't fix the problem, try restoring to factory settings and synching your apps. You'll lose the app data and settings, but if the problem is due to a corrupt cache or settings file, that should cure it. If not, then the iPhone has probably developed a hardware problem in which case you'll need to take or send it to Apple.

Regards.

If he jailbreaks it, he could install all sorts of junk on it. There will be nothing that can scan the iPhone for any such garbage, so your only options are either to 1) keep the iPhone out of this individual's hands or 2) restore it on a regular basis.

Regards.

A software keylogger would probably record keystrokes and take a screenshot of Phone monitor in stealth mode.

See more about How to Detect If a Keylogger is Installed:

http://www.myjad.com/detect-installed-keylogger.html

a keylogger's purpose is to collect activity the users performs on the device

and spy and not be noticed

producing heat and making it act funny would beat that purpose

often people see bugs or otherwise behaviour they don't understand as virus, hacking, keylogging, spyware, malware, trojan horse or whatever term he or she been exposed to by media and friends of late

Do a spotlight search for "Cydia". Have you let someone have unattended access to your iPhone for more than a half-hour?

Your link has absolutely nothing to do with the possibility of a keylogger on an iPhone.

I'm curious... how do you think your link is pertinent to this iPhone discussion?