I'm 62 and every now and then I get these redish purple spots on my arms, they don't bleed but look close to bleeding, what causes this?

Get is checked pleas. It is difficult to assess without looking at these spots It might be due to pressure on the arm, or due to blood problems resulting in reducing number of Platelets (tiny pieces that helps preventing bleeding) in the blood. Your doctor should be able to check the spots and arrange some testing to find the cause.
Spots . There could be multiple reasons for reddish purple spots like blood vessel becoming fragile with age and bleeding on minimal trauma especially if one is on blood thinners . Sometimes decrease in platelets ( kind of blood cell ) can also cause similar presentation. Consult your doctor for examination and maybe blood test . .
Capillary fragility. and thinning of the epidermis will cause "micro-bleeding" under the skin: normal in aging unless you are having bleeding or you are on anticoagulants.