Question: If I am messing around with XCode and trying to learn Objective-C, does it pose any threat to my system if I routinely forget to release objects? What is the real consequence of not releasing objects? If I restart my computer will these memory leaks persist?

I am mostly messing with NSStrings and NSTimers and things like that, nothing serious. I'm just concerned about it messing up my computer.

Is there any way to check if there are unreleased objects? What is one to do if they want to check a bunch of code to see if there are any of these memory leaks?

Answer: 
The only "threat" is that your program will eat up a large chunk of your available memory, which will cause your computer to go slow and your hard drive to thrash until the system reclaims the memory when the program ends. It makes things pretty unpleasant when a program uses more memory than it has to. Not dangerous — just really annoying.
First of all: all processes run in their own virtual memory, so when you kill the process it's memory is being returned to the system no matter how many leaks are there.

Second. By not releasing the object there is no way to tell the system that an object should be freed and that's why all allocated objects will remain in memory even if they are already unnecessary.

Try to start from something like C and not Objective C, cause it's obvious to me that you have no idea what the pointers, RAM and so on really is.