On my iphone5/ios7 I used the demo without BridgeIt installed.

1. The Page Not Found error dialog appeared when I tried to use the photo demo
2. Then the BridgeIt HTML dialog appeared for Missing BridgeIt, which allowed me to go to the App store to download it.
3. Then I switched back to the web page, closed the HTML dialog, tried to Take Photo
4. Switched to BridgeIt, but nothing but the icon displayed for approx. 15-20 secs? Then A dialog appeared asking if I wanted to Trust BridgeIt, Clicked Yes.
5. Then camera view could be seen but on top was a dialog saying "Welcome. Thank-you for using ICEmobile-SX. Return to your web page? (OK/Cancel)", even though I hadn't taken a picture yet.
6. Clicked Cancel, took a picture, it returned to the web-page and my picture thumbnail was there, but the orange html popup warning that BridgeIt wasn't found was also visible again.
7. Dismissed the popup, then noticed that the bridgeIt app banner was visible at the top of the page. Closed that.
8. Subsequent photo taking didn't result in the popup or banner appearing again.

Note that if I open the BridgeIt app immediately after installing it, it presents the "Thank-you for using ICEmobile-SX, return to web-page dialog immediately". Clicking Cancel, then going to the demo page and taking a picture works perfectly, with no incorrect orange HTML dialog showing up. What is the "Welcome, thank you for using ICEmobile-SX" dialog even for? Seems to cause problems...

Also, if I try to select a picture from "Album" it fails with "This app does not have access to your photos or videos...".

iphone 4s IOS 6 with BridgeIt installed.
Missing BridgeIt native features prompt occasionally occurs after taking photo with app and submitting the "Use" button.
Missing BridgeIt also occasionally occurs after pressing Cancel button in reality view mode of Augmented Reality app. Not able to reproduce either issue reliably with or without cleared cache.

I'm able to reproduce an initial delay with launching BridgeIt on iOS 7: install BridgeIt, but do not open. Then, return to Safari and launch BridgeIt with camera. This first launch from Safari is very slow (unlike opening BridgeIt directly from the home screen) and the browser pageHide event does not take place until the first dialog in BridgeIt is shown. This appears to be some sort of deadlock within iOS as neither the browser nor BridgeIt are receiving events.

Other developers have reported the URL scheme launch delay in iOS 7. I am about to test iOS 7.1 beta.

BridgeIt detection may fail in some rare cases, but recent testing shows that it is generally working well.