IME a small bubble should not affect the accuracy at all. However, a bubble larger than 1/4" or so could already prevent the needle from swinging freely, introducing a completely random error that might be 5 or 180 degrees depending on how exactly you hold the compass and how the bubble moves inside the capsule.

A bubble this size is pretty bad. That compass needs to be repaired or replaced, either way it cannot be expected to give accurate, consistent bearings:
http://tasmania.bushwalk.com/forum/downl...4&mode=view

While a small bubble does not necessarily mean the end of a compass it's still a cause for concern. A small bubble is likely to grow bigger in cold temperatures and high altitudes.

Is it possible to repair a copass with this sort of defect in the field? I'm not sure. If there is really no other way you could poke a small hole and drain the liquid from the capsule. Unfortunately, that does not seem to work well in my admittedly limited experience.

Generally speaking, an accuracy of 2 degrees would be considered excellent, 3 degrees still acceptable from what I've been taught about land navigation. Keep in mind that even a compass in perfect working condition isn't really capable of perfect readings. IIRC, a top-notch prismatic compass has an ideal accuracy of +/- 0.5 degree. A good mirror or lensatic compass somewhere between 1 and 2 degrees. A baseplate 3 degrees or so.

This is the inherent accuracy of the compass and its sighting system (or lack thereof). It does NOT take into account user error or slight mechanical defects (loose bezel, slightly offset sighting mirror/sight line etc.).