- There's no Bitcoin wallet. Most incidents happen with stolen or lost wallets. Bitcoinica holds all the money and coins in traditional banks and other exchanges (currently only Mt. Gox).
- Bitcoinica runs on Heroku. Generally apps hosted in the cloud are more secure. Ruby on Rails itself is very secure too. (protect_from_forgery, html escape, force_ssl, etc)
- No account minimums. If you're unsure, you can deposit $1 first and try to do some trades.
- Margin trading. This reduces risks. You don't have to deposit 100 BTC worth of USD when you want to long/short a 100 BTC position. 20 BTC is enough. Only when you lose a lot, you can consider adding more margin.
I think trust is a common problem for all websites like Bitcoinica. That's why we designed the platform in the way that attempts to solve the fundamental problems.
There's instant deposit and withdrawal too. You can transfer money from Mt. Gox when you want to trade and transfer it back after you close your position. (Assume that you trust Mt. Gox.)