Speaking as someone who is actively working on setting up an online wallet. I can understand your concerns. It's also our biggest challenge (to build trust)
As someone who is obviously against the idea. What would make you feel more comfortable with the idea?
Assuming you're an honest individual I can still forsee the following problems.
1. How can you protect the bitcoin private keys in the wallet from...
a. Disgruntled employees (assuming you'll need employees)
b. Someone at the data center where your servers are hosted.
c. The backups you'll need to make. Who holds these ?
2. You're going to be constantly under cyber attack.
a. Who examines your code ?
b. Your software stack i.e. the 3rd party libraries you use how will you check that no-one inserts a specific attack on your site via a library upgrade.
c. How about your personal computers a hacker could gain access and use a keylogger to get root passwords ?
3. If you do well you'll be holding a significant amount of cash for other people that can easily be transferred and anonymized. You've also made yourself public on your site.
It's possible someone could attack you personally to get at the bitcoins. Have you thought about that ?