Take all the 'security' precautions you can, and don't be put off by parents of one toddler thinking you're being a bit neurotic. We had baby gates on virtually every doorway for a couple of years, so we could quickly fence off various areas. A huge playpen, too, useful in all sorts of ways. It's so easy to be distracted by one toddler and not notice that the other is up to mischief.
Be prepared for them to help each other out - two toddlers can climb higher if one clambers on top of the other. They can get over baby gates this way after a while, so keep an eye on them all the time. We had a trainee nursery nurse one afternoon a week - she had lots of energy and gave me a bit of a break - might be worth asking around.
When you're out and about, it may be worth dressing them differently, even if you dress them the same at home. When one runs off, you need to know INSTANTLY which name to shout. Training them to walk nicely on reins in approximately the same direction was something we never managed, although a friend with triplets used to do it fairly successfully.
You may feel that you can't do things that friends with one toddler can do - ours didn't go swimming for ages as there wasn't a suitable session when we could both take them. Not a problem in the long term, both started lessons when they were at primary school and can swim like fishes now.
It will be fine, though, toddler twins are huge fun, and we enjoyed nearly all it it! When anyone says "double trouble" to you, just give a big smile and reply, "no, twice as nice."