Exactly why I pay over $100 a month so my Dad has a supplemental Medicare policy. You (or someone) should look into it for your grandmother. If you're expecting great things from government provided medical coverage, you're going to be greatly disappointed.
BTW, the "vein" missing problem happened to me when I was personally paying for the bill - Medicare has nothing to do with it. That's why experts recommend there is ALWAYS another friend/family member in the hospital as much as possible with a patient to monitor what happens. There was an interesting (and very scary) article in Reader's Digest a few months ago regarding hospital mistakes.
Hope your grandmother's OK!!