The following things should be avoided.
Chocolate - this can be very toxic for dogs. Generally the darker the chocolate the more dangerous it is. Symptoms can range from vomiting to severe seizures. If your dog eats chocolate contact a veterinary surgeon, try to keep the packaging handy as this will help in deciding whether treatment is required. If treated early most cases will make a full recovery.
Raisins and Grapes - these are very toxic to dogs and cats. They can cause irreversible kidney damage and some cases have been caused when only a small amount has been eaten. Prompt treatment is required after they have been eaten but the symptoms may only appear after a few days.
Lilies - These can also cause irreversible kidney damage in cats. All parts of the flower are poisonous including the pollen. These flowers are best avoided if you have cats.
Also be careful not to overfeed your dog on Christmas leftovers. The increased fat in these often causes an upset stomach and in severe cases may result in a stay in hospital.
Decorations, string and ribbons - these may prove enticing to dogs and cats who frequently will play with these and possibly eat them. Over the years all manner of foreign bodies have had to be retrieved from dogs and cats.
Be careful not to over-exercise your dog over Christmas. As tempting as it is to get out of the house and walk your dog more, try not to suddenly increase their exercise. This is especially important in older and stiffer dogs.