As I've been off for work and being sick, I'm going to roll the remainder of December with January. Sorry
The Full Moon is 17 December and Last Quarter 25 December. New Moon is 1 January, First Quarter is 8 January, Full Moon 16 January and Last Quarter 24 January.
C/2012 S1 ISON has disintegrated, several attempts have been made to find the remnants, if there are any, they are below magnitude 22.
Comet C/2013 R1 Lovejoy as seen at astronomical twilight in the morning from the New Mexico scopes. Click to embiggen.
Terry Lovejoy's fourth comet is still performing well than expected. Currently around magnitude 5 it has an awesome tail with great detail spanning several imaging fields.
The comet is visible only from the northern scopes.
Unfortunately, for the rest of December and the beginning of January it is only 19 degrees above the horizon at astronomical twilight, meaning that only T5 and T11 can image it.
The comet starts in Hercules and moves into Ophiuchus. Lovejoy has no particularly interesting encounters, but it is such a great imaging object that none are really needed.
C/2012 X1 LINEAR is still bright, around magnitude 9. It is not far from Lovejoy (see map aove) but nettwer position at around 26 degrees from the horizon at astronomical twilight. On December 20 the comet is 1 degrees from magnitude 12.7 galaxy NGC 6012. On December 26 the fading comet is near magnitude 11 planetary nebula IC 4593.
Comet 154P Brewington is is around magnitude 10, and will fade to magnitude 11 over January. It is visible from all the nothern iTelescopes. Despite being in a target rich area, it has no interesting encounters, but is reasonably placed for imaging in the early evening as it move from Pegasus to Andromeda.
Comet C/2013 V3 Nevski is brighter than predicted, around magnitude 10, but diffuse, it is well placed for the northern iTelescopes high in the morning sky, moving from Leo Minor to Ursa Minor.The image shows the view from Mayhill New Mexico at astronomical twilight in the morning. Click to embiggen.
On December 21 comet Nevski is 0.3 degrees from magnitude 11 galaxy NGC 3414. On December 24 it is over 1 degree from magnitude 10 galaxy NGC 3486. On 9 January it is over 1 degree from magnitude 11 galaxy NGC 3665. On 18 January the comet is 0.5 degrees from magnitude 10 NGC 3675, then on January 22 it is 1 degree from magnitude11.6 galaxy NGC 3614, finally on January 25 it is 1.5 degrees from magnitude 10 NGC 3726.