We're submitting and app to the app store and polishing up the app description. If you used something like "This is the James Bond of email services" would that be a copyright or trademark infringement?
It would certainly not be copyright infringement. Copyright law explicitly says that you cannot have a copyright to a general idea, a name, or a title.
It might be trademark infringement. Usual disclaimer: I am not a lawyer.
On the one hand: My understanding of trademark law is that for it to be trademark infringement, it has to have the potential to confuse potential customers. Like if you started your own hamburger restaurant and called it "McDonald's Hamburgers", you would clearly be guilty of trademark infringement. If you are not trying to trick people to come to your restaurant instead of a real McDonalds, it certainly sounds like you are. But if you started a muffler shop and called it "McDonald's Mufflers", McDonald's Hamburgers would be unlikely to successfully sue you for trademark infringement because no one is going to buy a muffler as a substitute for a hamburger. You are not costing them any sales.
In this case, it is unlikely that someone will confuse your email service with a spy novel, or that they will subscribe to an email service instead of buying a spy novel.
On the other hand: The publishers of James Bond novels might conceivably bring a case against you if your advertising could be construed as indicating that your service has some connection to their novels -- like if it leads people to believe they can get copies of the books emailed to them or some such -- or if it implies that the publishers have endorsed your service.
And people can bring lawsuits even when a rational person would say they have no valid case. If you're a small company, then the time and cost of defending yourself in court could destroy you, even if you win in the end. (Sometimes courts orders the loser to pay the winner's legal bills, but often not.) There are plenty of horror stories out there of companies bankrupted by lawsuits even when they won, or that ended with the suit being dropped.
The fact that you're asking on this forum tells me that your company does not have a team of lawyers on staff to handle such questions. Which means that if someone did sue you, you'd be scrambling to pay the legal bills.
So my advice would be: Don't. There must be a million other slogans you could use. You could even use variations of the same idea. Just call it "the master spy of email programs" or whatever the idea is that you're trying to convey.
Which, by the way, brings up that it is not at all clear what you mean by saying "the James Bond of email services". Are you trying to say that your email service helps you spy on people? That using it is a dangerous and difficult adventure? The slogan is probably weak anyway because customers will have no idea what it means.
Nope. It isn't copyright infringement.
You aren't using a representation of James Bond in any way, only the idea of James Bond. Ideas are not copyrightable.
For further information see this page on characters and copyrights from Aspect Law Group.