Is it acceptable to point out job offers in my graduate school application? Just some background: I am currently an undergraduate and I will be graduating next year. As of now I have an internship position doing research in my favorite area. This will extend into a job offer (doing the same thing) once I graduate. My employer will not require a higher degree for me to continue doing research, but I want to acquire at least a Masters, likely a PhD as well.

In order the strengthen my graduate school application, I am thinking of mentioning this situation in such a way as to demonstrate my determination and commitment to higher studies. For example, I can mention that I am already doing research in this area and that I have a guaranteed position doing research in this area upon graduation, without needing additional degrees. However, instead of taking the comfortable option, I want to invest in my knowledge and take the harder option which is going to graduate school and acquiring a higher degree. Would this be helpful or possibly hurtful?
It's acceptable, but it probably won't help and could even easily hurt your application. It might be taken as a threat to the department, i.e. it's like saying, "I could take this fabulous industry job I've been offered if you don't admit me!" I might find this off-putting if I read it in an application. Departments aren't usually short of applicants, so a reviewer might just put your application aside thinking, "OK, you just go ahead and take that position. I have 50 more applications in this pile over here to go through."

Determination to do research isn't the most important factor in demonstrating your ability to complete a Master's or PhD program. The internship by itself helps show your passion for research, and maybe helps show that you're capable of it, but the idea that you're highlighting your willingness to bail on the internship in order to pursue a higher degree might say to some committee members that you're also willing to bail on the graduate degree program if something better comes along (like a nice offer from Google or Microsoft in you're in Computer Science). 

I think you're better off using the current internship to show that you are able to make progress in research, and leave the idea that you've been offered a job extending that research aside, lest you come off as pretentious or threatening. There are lots of suitable graduate school candidates with internships or prior research experience who might also be suitable to the same program. Use yours to show that there's something different about you.