This is a great chance to see exactly why Charles Messier decided to include this cluster in his catalog of comet-impostors. Comets with bright tails are unmistakable, but LINEAR's tail is still extremely small and faint. Only a few keen-eyed observers have managed to spot the tail from pristine dark sites, and even astrophotographers find it challenging to capture. Otherwise, the comet looks like a nearly circular ball of light with a somewhat brighter center — very much like a typical globular cluster viewed through binoculars or a small telescope.
It's also an extraordinary opportunity for astrophotographers, especially ones in Europe who can capture the closest approach. Similar as these objects appear through the eyepiece, they could hardly be more different in a camera. Astrophotos easily resolve M3 into individual stars, while showing that the comet is a ball of gas glowing with a strong greenish tint.
The Moon is just a little past first quarter, so its light shouldn't detract too much from the view of these bright objects. In fact, the moonlight should be only a minor addition to the normal skyglow of most suburban sites. You can also wait for the Moon to set around midnight local time, but by then the comet and cluster are getting quite low in the sky. If you do take a photo, please share it with us
Our detailed chart showing the comet's motion across the sky is still available as a printable PDF file.