Anything boiled should be safe to drink, and the dust on the cups shouldn't really be a problem, either. In my experience, most things in India tend to have a layer of dust on them no matter how fastidious you are. :)
I disagree with @hippietrail about using "popular" places to judge their safety - popularity can be an indicator, but it's not a guarantee that you won't get ill. Most of the reason that travelers get sick is because they're consuming something their bodies either can't handle or haven't built up tolerance to. (Also, keep in mind that what the dine-in portion of a restaurant looks like isn't always indicative of what the kitchen looks like. I once was in a restaurant that was impeccable in the part where the customers were, but I saw the door to the kitchen swing open and there was a standing measure of dirty, muddy water with insects and dirty dishes everywhere.)
Cold drinks and foods are usually more dangerous: as others have pointed out, you should be careful about fresh fruits or vegetables that you haven't prepared, and always either decline ice in your drink or specifically ask if it was made from filtered water (you might need to use the term "R/O water" - filtered through reverse osmosis). Ice cream / kulfi that isn't pre-packaged can be dangerous, too; street vendors typically don't wash their hands often.
The bottom line is to be cautious without detracting from your sense of adventure and experiencing everything India has to offer. Ask if you have questions about the way something is prepared, be observant about the conditions of your food and its preparation, and when in doubt, go with your gut (no pun intended).