Don't let the date drag on indefinitely. Kids this age don't need marathon playdates. Most will get bored and cranky after one hour -- 90 minutes, tops.
Don't forget: Location matters. Toddlers can get possessive when they're on their own turf, especially when it comes to sharing their toys. Holding the playdate in neutral territory, such as a playground or the children's room at the library, will limit the tears and cries of "Mine!"
Don't hover. Always stay close by to supervise, but intervene only when you absolutely have to (such as when one kid is hitting the other or they start calling each other names). If you step in during every little disagreement, your child won't learn how to work out his problems for himself.
Don't make sharing harder than it is. Minimize meltdowns by warning your toddler ahead of time that you expect her to share her toys. However, if she has a special possession you know she'll resist handing over, put it away until after the playdate. Set out toys that are easy to share, such as balls or blocks, or give the kids a bunch of the same type of toy, like dolls or cars, says Carren Joye, author of A Stay-at-Home Mom's Complete Guide to Playgroups. Even better: Suggest a gear-free activity such as dancing.