The Contents of my diaper bag when going out..
Diapers: Carry at least one for an hour or more depending on the time you are going to stay out. Personally suggest carry more than needed in case of emergencies.
Nappy Changing Pad: This is very useful to avoid slipups during diaper change and also on unclean surfaces.
Wipes: Very helpful to clean up the baby when changing the diapers.. not just the baby wipes, if you can keep disinfectant wipes for yourself, in a small travel pack, it would be great.
Burp clothes/bibs/clean cotton clothes -- To wipe the baby's face and mouth when feeding.
A change of dress for the baby.. In fact, a couple or more dresses would be best.
If in winter, keep a sweater, muffler/cap, socks, mittens hand in case you might stay back a little late in the evening.
If the baby is bottle feeding, then carry enough bottles and formula/milk sufficient for the feeds.. Also, a flask full of warm water just about right temperature to use for mixing the formula. -- Clean the bottles immediately after the feed, if possible with warm/hot water so that you can re-use in case you stay longer than expected.
If the baby is on solids -- small containers to carry the food, the bowl, spoon, glass, or sipper.
Water bottle -- boiled and cooled drinking water or mineral water/nursery water whatever you use for the baby.
Pacifier if the baby uses one.
The baby's pediatrician's number, medical record book ( if in India), a phone book with all the numbers handy or a mobile with the numbers stored.
Do not forget to carry at least a couple of toys, a comfort object like a blanket or whatever.. and also keep something to keep the kid occupied like a book to read, a soother to chew on.. :).
A small blanket/throw/rug -- for the times when you want to put the child on ground to play.
A change of dress for you. -- In case the baby spits on you or vomits.
Also, keep a few plastic covers/an extra bag to carry the soiled/used clothes.