I scanned testcases for patterns where Loggers could potentially be collected by GC and cause a test failure. See Logger.getLogger API :
http://docs.oracle.com/javase/7/docs/api/java/util/logging/Logger.html#getLogger(java.lang.String)

These tests probably deserve some attention :

test/tools/jar/UpdateManifest.java :
    - Logger.getLogger("java.util.jar").setLevel(Level.OFF);
    
test/java/util/logging/Logger/getGlobal/TestGetGlobalConcurrent.java
    - Logger.getLogger(Logger.GLOBAL_LOGGER_NAME).info(messages[i]);
    
test/java/util/logging/ParentLoggersTest.java
    - Logger.getLogger(LOGGER_NAME_1);
    - Logger.getLogger(LOGGER_NAME_2);
    
test/java/util/logging/LogManager/RootLogger/setLevel/TestRootLoggerLevel.java
    - 5-6 cases that need checking ?
    
test/java/util/logging/CustomLogManagerTest.java
    - line 46 - 48
    
test/closed/sun/security/ssl/sanity/compatibility/manual/Https.java
     - closed testcase. may be suspect.