Spoiler Alert - Click to Toggle
Yes, I was bothered by Tom Anderton being able to use his detached eyeball to pass through security and get into "the temple" despite him being a fugitive on the run. This was a glaring plot hole I noticed the first time I saw the movie. The one involving how Anne Lively was murdered annoyed me even more.
Even if Tom Anderton's security clearance was still good, detached eyes aren't going to be useful at all unless they're kept in cold storage. Even then they're only going to be viable for a limited amount of time. Without continuing blood/oxygen supply a detached human organ will quickly die and then start decomposing. The unique blood vein pattern in the retinas used as a security fingerprint of sorts will change in that process of decomposition. Dead eyes often cloud over to where the security beam wouldn't be able to see the retina in the back of the eye ball.