I need to enter precise geographic coordinates for my data, not simply click on the map. Is ArcGIS Online / Collector capable of this?
Currently in AGOL / Collector, nope. Using those I think you'd have to tap or click based on an estimate, then drag the point around and watch the coordinates change to get it somewhere close. You could have the collector tap roughly where it is, then fill in some latitude and longitude attributes for someone else's reference. Or use device GPS if you're collecting where the device is and you can get the accuracy you need from the device.
Thanks so much for your reply! Actually, I found a work-around: using the "measure" option, "location" tool in AGOL allows me to hover until I see the precise coordinates I need---then add my point. (And yes, in the field this should be no problem... I was aiming to avoid returning to the field to re-acquire data whose coordinates I had prior to learning AGCollector.)
Retrieving data ...