Protecting yourself against these travel and apartment scams is not too difficult if you go in cautiously.
For the airline tickets scams, I would just suggest avoidance. Unless you can make personal contact or somehow guarantee that the tickets are real, or the person is a licensed broker, then it's just not worth the risk.
Vacation apartment scams are a little harder to avoid (if you don't want to stick to well-known, and expensive, hotels). In order to protect yourself against scams, you should try to request referrals or do some searches for the name and email address used (and possibly the message). Some scammers are lazy, or try to pull the same scam on many marks at once. A Google search can save you a lot of time and money.
Tineye can save you a lot of trouble too. It's worth it to save the pictures and then run them through the search site. A lot of scammers just steal pictures. If you see them coming up for nice apartments far away from your destination, then you should know that something's up.
You should also insist on a phone number to see if they're even in the area that they claim to be in. If they try to avoid talking on the phone, then something may be up, or they may not be who they say they are. If they've set up an identity as a kindly old woman, they may just cut you loose before trying to find someone to talk to you.
If you have any contacts in the area, try calling them ahead of time and ask about the neighborhood and the apartment. If you don't know anyone there, then try using Google Maps to look at the area and then look around for any online communities that might be able to help. There's nothing better than some local opinions.