Is it legal for children to go out on mischief night and throw toilet paper and throw eggs as long as it does not do physical damage to the property?

There's a difference between toilet paper and eggs, because eggs can permanently stain some types of siding, and that does damage the property.  I have seen this as an issue in an actual lawsuit.

Another legal consideration is trespassing.  If someone tells your child to stay off their property, that needs to be respected, and that includes not throwing things onto the property.

Finally, it's possible to look at "papering" as littering.  If law enforcement has to respond to a problem caused by your child, it's quite possible that law enforcement will find a way to give you a problem caused by your child.

Eggs do physical damage to property. Plus, depending on where they go on the property, it may be considered trespassing.  Further, such acts are considered vandalism -- no matter if the damage is permanent or otherwise. You are quite a smart parent for asking because it shows you care!

See the following press release from the Police Department of Milford, Connecticut.  It will prove quite helpful to you to ensure your children have a great time on Mischief 2009 but to avoid vandalizing property:

http://www.milford-ct.gov/Public_Documents/MilfordCT_Police/PressRelease/F1C8F2D9-3B9ACA00.1/Mischief%20night%202009.pdf