Probably the worst way in which spill can occur is when recording the basic tracks of a band's performance while the vocalist sings a guide vocal. Without the guide vocal the band would have to be very well rehearsed and disciplined to give a good performance, and even then it would probably be professional rather than inspired.
Over the years, the guide vocal has become a standard part of band recording technique, and often it has been found that the vocalist is more relaxed than during the vocal recording proper and gives a better performance.
But suppose it is the intention that the guide vocal be replaced, what will happen if the singer's voice spills into the other mics, and where will the problem be centred? To answer the second question first, the prime candidates for picking up spill in a conventional band recording would be the drum overheads as these mics are furthest from the signal source and would have more gain applied than any of the other drum mics, or amplified instrument mics.
A miked acoustic guitar or piano would also be a problem (particularly if the singer is playing it). It has been common practice for many years that a song won't necessarily be entirely finished when the band comes into the studio, and often it won't even be started. Hence the vocalist doesn't necessarily have a complete grasp of how he or she wants to sing the song, and it is likely to come out a little different each time. Also, it isn't impossible for the words to change between the guide vocal and vocal recording proper.
Either way, whatever differences there are between the guide and final vocal will show up in the spill, and they might be very audible. The classic example of this is Led Zeppelin's 'Whole Lotta Love' where differences between the guide and the final vocal are very clearly audible towards the end of the track.
Another way in which spill can present a problem in recording is if an instrument has been recorded alongside other instruments, but then it is decided that its contribution isn't needed. So the engineer pulls the fader down and, guess what, the instrument is still audible in the spill in the other tracks. This sounds bad because it is so clearly a fault, and the degree to which it can be tolerated is minimal.
The third way spill can make an unwelcome intrusion is when a track is processed by EQ or another effect, and spill from another instrument on that track is processed too. It is perfectly possible to find, for instance, that the amount of EQ you would like to apply to a track is limited by the undesirable effect it is having on the spill from another instrument that has been picked up on that track. Recording engineers do of course learn the fine art of compromise so it isn't necessarily the end of the world, but it's a problem that you could do without.