As an instructor, you must be able to demonstrate good throw rope technique. You should be able to toss a rope via various methods with reasonable accuracy. It is important to hit the swimmer within arm's reach, don't make them swim for the rope as this can be dangerous. This is one skill you will need to practice regularly to become proficient in.
The best way to ensure accuracy is to practice frequently. Start with static targets until you get your distance and accuracy down pat. Avoid tossing the rope too far since it may get tangled downstream. I like to drop the rope about 6' over the swimmer. This prevents them from grabbing the end of the rope and also helps prevent the rope from getting snagged downstream. Once you have mastered static targets, practice on moving targets. When fetching swimmers cascading downstream, you need to lead them a little bit. Bear in mind, a bulls eye is 2' from their chin - basically within their reach. Use the right tossing technique, underhand for large ropes and overhand for small ropes or when sitting in a boat. Sidearm tosses are much more tricky but sometimes essential if limbs are in the way.
Practice with different types of throw lines: big lines, small lines, waist lines, and coiled lines. This can be a fun activity on non-crowded streams - perhaps during a lunch break. If you are a large strong guy, you probably will have the best luck with the full size rescue bags and the underhand toss. Tossing these bags is a great deal like tossing horseshoes. Smaller individuals may have some difficulty with the weight of a large bag, that's cool because there are many small sized bags. These are tossed overhand - just like a baseball. They are great for close by rescues. With long ropes, you really need to avoid paying out too much line. Small bags are easier to control the length of line fed out. The diameter of the line doesn't really impact accuracy but makes a huge difference in rope handling. I would much rather hang onto a 3/8" line than a 1/4" line any day.
Good footing makes a big difference as well. If you are trying to balance yourself when tossing the rope, it's hard to be very accurate (not to mention keeping yourself from being pulled in when the swimmer grabs the line). The distance away from the target makes a difference as well. Off by 2° doesn't matter much at 10' but is probably a miss at 50' or more. It is important to wear gloves during rope work when it gets cold outside. First off, gloves protect your hands and secondly cold hands are stiff and inflexible (plus it hurts). Cold hands make accurate throwing quite difficult. Obstacles like low hanging branches, large boulders, etc. make accuracy far more critical and certainly more challenging.
