My husband downloaded all kinds of iPhone apps that mimic the barcodes on my rewards cards such as AirMiles, Aeroplan, Longo's, Hallmark etc. Are these types of applications secure?
There is no easy way to know for sure. Apple does vet applications, but not for many privacy concerns.
If someone spent the time to test such an application out on a wifi network, and sniff the network traffic, then it's possible to detect if the application is calling in to some central server, but even that won't detect everything.
It is possible to reverse engineer the software, but that's an expensive and/or time consuming process, so it's unlikely that someone would take the time to do that.
This is an area where developers could use some help. If a third party company vetted their software source code (such as Verisign), then they might be able to extend assurances to their users.
Until then, caveat emptor.
That depends on what you mean by "secure". If you mean "will they steal my membership numbers", probably not. For one thing, they risk being found out and getting caught. For another, a membership number by itself is usually not spectacularly useful. What are they going to do, save money at Safeway? Steal your free sandwich? Oooooh, scary.
Ask yourself: what memebership cards could cost you if you lose them? If you have some where this is a problem, be more concerned.
If you mean "can they steal my membership numbers", that's more "probably". I don't have an iPhone, but Android phones (at least) list the things an app is allowed to do. If it's allowed "full Internet access" it might not be secure. If not, it's probably fine (unless they sneak something in an update that you don't notice).
One other point - if they have your number most of the rewards sites still need a password to get in to administer the plan. If they don't try to crack the admin site the only other thing they could do is get you millions of points on your plan. In which case you might get a "friendly" notice from the company running the plan about suspicious activity on the account which may also lead to it being suspended.