The International Components for Unicode (ICU) implement the Unicode Standard and many of its Standard Annexes faithfully and are updated to a new Unicode version soon after its release. Usually, the ICU team participates in the Unicode beta process by updating to a new Unicode version in a branch and testing it thoroughly. In the past, this has uncovered problems that could be fixed before the release of the new Unicode version.
One notable exception to ICU implementing all of Unicode is that it does not provide any access to Unihan data (mostly because of low demand and the large size of the Unihan data).
For the last several updates, there is a change log here. In short, most of the ucd .txt files are copied into the ICU repository, either without modification or, for some files, with comments removed and lines merged to reduce their size.
Some of the data files are not part of the Unicode release but are output from Mark's Unicode tools. See http://sites.google.com/site/unicodetools/
Note: We have looked at using the UCD XML files, but did not want to rely on them alone until there was a way to verify that they contain precisely the same data as the .txt files. Also, using the XML files would require a partial rewrite of the existing tools. (There is an outdated, experimental, partial UCD XML parser here: http://bugs.icu-project.org/trac/browser/icuhtml/trunk/design/properties/genudata)
The ICU Unicode tools parse the text files, process the data somewhat, and write binary data for runtime use. Most of these tools live in a source tree separate from the ICU4C/ICU4J sources, and link with ICU4C.
The following steps are necessarily manual:
New properties (whether they are supported via dedicated API or not) should be added to the Properties User Guide chapter.
The ICU test suites include some tests for Unicode data. Some just check the data from the API against the original .txt files. Some tests simply check for certain hardcoded values, which have to be updated when those values change deliberately. Other tests perform consistency checks between some properties, or between different implementations.
There is a program as a part of CLDR that uses regular expressions to test the segmentation rules and properties (LineBreak, WordBreak, etc). That is, there is a regular expression corresponding to each of the rules, and a brute force evaluation of them. That is used to generate the tables and test data. The segmentation rules in ICU are later modified by hand to match the specifications. That has to be done by hand, because there are some areas where the rules don't correspond 1:1 with the spec. There are a series of ICU consistency tests for those rules. ICU also includes regression tests with "golden files" that are used to detect unanticipated side effects of revisions to the rules.