Are Factory Unlocked iphones any good? Will there be problems?

I'm thinking about getting some iphones for my mother and her boyfriend for Christmas. (I know, its way early to be thinking about any presents, but i'm just browsing around). Since i do not know exactly what carrier they are with i'm just looking around at Factory Unlocked iphones, say i do get the phones, They're shouldn't be any problems when they go to use the phone with their carrier will they?
Also, (Just wondering) How will the i know the seller is telling the truth that the phone is unlocked, if i do get the phones, will there be some way i will be able to tell if the phone is factory unlocked?

There's nothing wrong with factory unlocked phones. As soon as you're mum and her boyfriend put the sim they use in there it will work straight away no problems at all.

Also there's no way to tell apart from testing different sims yourself or I'm pretty sure it says somewhere in the settings. If they are not though and you've been lied to, you can get them unlocked at some places for a charge, or if you know someone who can give you unlock codes then you can do it yourself for free or very cheap!

Factory unlocked phones is awesome, you can use it as per your desires…

Factory unlocked