Review of past items is generally disallowed. Adaptive tests tend to administer easier items after a person answers incorrectly. Supposedly, an astute test-taker could use such clues to detect incorrect answers and correct them. Or, test-takers could be coached to deliberately pick wrong answers, leading to an increasingly easier test. After tricking the adaptive test into building a maximally easy exam, they could then review the items and answer them correctly--possibly achieving a very high score. Test-takers frequently complain about the inability to review.
Although adaptive tests have exposure control algorithms to prevent overuse of a few items, the exposure conditioned upon ability is often not controlled and can easily become close to 1. That is, it is common for some items to become very common on tests for people of the same ability. This is a serious security concern because groups sharing items may well have a similar functional ability level. In fact, a completely randomized exam is the most secure (but also least efficient).
In order to model the characteristics of the items (e.g., to pick the optimal item), all the items of the test must be pre-administered to a sizable sample and then analyzed. To achieve this, new items must be mixed into the operational items of an exam (the responses are recorded but do not contribute to the test-takers' scores). This presents significant logistical, ethical, and security issues. For example, it is impossible to field an operational adaptive test with brand-new, unseen items. And each program must decide what percentage of the test can reasonably be composed of unscored pilot test items.