This is a follow up question to this question:
Update Android Support Library to 23.2.0 cause error: XmlPullParserException Binary XML file line #17
For people like me still using Eclipse without Gradle, I had this error with Android Support Library r23.2.0 running on pre-Lollipop devices (API < 21).
This issue has been fixed in r23.2.1 and I have been able to run my project on API level 16 successfully.
This version of the library for Eclipse is not available through SDK Manager anymore, however you can manually download it from this link.