Is it a problem to get a boob job if you are diabetic?

Nope. Diabetics can have a harder time healing wounds and with infections. These can be reduced by maintaining good control of your diabetes. Consulting with your endocrinologist or diabetes doctor prior to surgery can also help provide a safer and more predictable experience.
Maybe, maybe not... Risks of infection are higher in diabetics, but to decide the risks vs benefits, i would have the physician who manages your diabetes discuss the proposed operation in detail with your plastic surgeon. The magnitude of the increased risk will depend on a number of factors: your weight and the adequacy of your glucose control are just a few. Good luck!
No. I've done these for diabetic patients. As long as you are well controlled, your risk of surgical complications is only minimally higher than a non-diabetic. There's no reason you can't have this surgery if you are medically cleared.
No. The risk of infection is higher with any elective surgery if your glucose levels are not well controlled. We perform elective surgery on diabetics on a routine basis.
No, if... Well controlled diabetes is not a contraindication to breast augmentation and/or other elective plastic surgical procedures. Always best to check with your primary care physician or endocrinologist for “medical clearance” prior to surgery. Managing your medications around the time of surgery (to avoid hypo as well as hyperglycemia), while you will have altered oral intake, will be important.