How can I repair a worn and rusting dishwasher rack?
There are products designed specifically for this, like this one:

I haven't tried it - I actually have a kit but never got around to it...
I definitely would not use tape because if it comes off during a wash cycle and clogs the drain you have a real mess. The racks (doesn't matter what brand) vary by model. Even when you can get replacements, the cost is a significant portion of the cost of a new dishwasher.