List all things that destroy trust here and things not to do!

1. Appearance is everything! The first wrong thing you could do to destroy trust between your customers without even providing them any services, is to have an unprofessional site.

Make sure images are clean and clear

Pages load fast

words and pictures are not cluttered

Words are spelled correctly

Broken links are corrected

2. Not responding to emails or requets for more information. If the customer cannot get in contact with you, they are going to wonder if their order is going to be handled in this manner.

Post your ideas!!!

This has nothing to do with your online store, but I think it's vitally important for any online business.

A lot of customers will call the customer service directly. Some will be calling to find out if there's a real person behind all this; some will be calling to find a little about your products, your company history, etc. If you miss these calls, make sure they are recorded and you return them asap.

Although our store lists the office hours as M-F, 10-5, I just received a phone call from a customer and its 8:00 am, Sunday morning.

Customers never pay attention to calling times. We regularly receive phone calls at 6:00 a.m. and as late as 9:00 p.m. and our hours are listed 9:00 a.m. to 6:00 p.m., we even have an international calling page that lists the time a customer can call us from their location.
Contact is a big part of losing trust with customers. If you don't have communication you will not do well. Emails and phone calls should be returned no later than 24 hours after receiving them (except on weekends, where waiting till monday is just fine).
Also, not having your contact information clearly visible can be a lose in trust. You should have clearly visible or easy access to your emails, phone numbers, and business address.