I created a bundle that seems to be crashing randomly a few seconds after launching the app.
Java build is 1.8.0_40-b25

The stack trace looks similar to RT-24864:

Process: Application [17090]
Path: /Applications/Application.app/Contents/MacOS/Application
Identifier: com.app.Application
Version: 5.1.0 (5.1.0.94)
Code Type: X86-64 (Native)
Parent Process: launchd [291]
Responsible: Application [17090]
User ID: 502

Date/Time: 2015-05-22 18:07:30.430 -0500
OS Version: Mac OS X 10.9.5 (13F1066)
Report Version: 11
Anonymous UUID: 35B5D5AA-2851-D6C0-288C-5660426A6823

Sleep/Wake UUID: 69B1CCFB-2121-4609-8B6E-5042EA8B7169

Crashed Thread: 0 Dispatch queue: com.apple.main-thread

Exception Type: EXC_BAD_ACCESS (SIGABRT)
Exception Codes: KERN_INVALID_ADDRESS at 0xffffffff0000001a

VM Regions Near 0xffffffff0000001a:
--> shared memory 00007ffffff49000-00007ffffff4a000 [ 4K] r-x/r-x SM=SHM
    

Application Specific Information:
abort() called

Thread 0 Crashed:: Dispatch queue: com.apple.main-thread
0 libsystem_kernel.dylib 0x00007fff91635866 __pthread_kill + 10
1 libsystem_pthread.dylib 0x00007fff8dcb135c pthread_kill + 92
2 libsystem_c.dylib 0x00007fff99478b1a abort + 125
3 libjvm.dylib 0x000000010244923f os::abort(bool) + 25
4 libjvm.dylib 0x0000000102569c8c VMError::report_and_die() + 2250
5 libjvm.dylib 0x000000010244ae6a JVM_handle_bsd_signal + 1131
6 libjvm.dylib 0x0000000102447147 signalHandler(int, __siginfo*, void*) + 47
7 libsystem_platform.dylib 0x00007fff93bbe5aa _sigtramp + 26
8 libobjc.A.dylib 0x00007fff8fbe3097 objc_msgSend + 23
9 libglass.dylib 0x000000011fbf5fee -[GlassTouches(hidden) sendJavaTouchEvent:] + 1550
10 libglass.dylib 0x000000011fbf569e listenTouchEvents + 94
11 com.apple.CoreGraphics 0x00007fff8f3f62da processEventTapData + 614
12 com.apple.CoreGraphics 0x00007fff8f3f5f4b _CGYPostEventTapData + 185
13 com.apple.CoreGraphics 0x00007fff8f10739e _XPostEventTapData + 99
14 com.apple.CoreGraphics 0x00007fff8f107486 CGYEventTap_server + 81
15 com.apple.CoreGraphics 0x00007fff8f3f6039 eventTapMessageHandler + 46
16 com.apple.CoreFoundation 0x00007fff907ea9c4 __CFMachPortPerform + 388
17 com.apple.CoreFoundation 0x00007fff907ea829 __CFRUNLOOP_IS_CALLING_OUT_TO_A_SOURCE1_PERFORM_FUNCTION__ + 41
18 com.apple.CoreFoundation 0x00007fff907ea79e __CFRunLoopDoSource1 + 478
19 com.apple.CoreFoundation 0x00007fff907db7d6 __CFRunLoopRun + 1830
20 com.apple.CoreFoundation 0x00007fff907dae75 CFRunLoopRunSpecific + 309
21 com.apple.HIToolbox 0x00007fff95f9ba0d RunCurrentEventLoopInMode + 226
22 com.apple.HIToolbox 0x00007fff95f9b7b7 ReceiveNextEventCommon + 479
23 com.apple.HIToolbox 0x00007fff95f9b5bc _BlockUntilNextEventMatchingListInModeWithFilter + 65
24 com.apple.AppKit 0x00007fff9791f24e _DPSNextEvent + 1434
25 com.apple.AppKit 0x00007fff9791e89b -[NSApplication nextEventMatchingMask:untilDate:inMode:dequeue:] + 122
26 com.apple.AppKit 0x00007fff9791299c -[NSApplication run] + 553
27 libglass.dylib 0x000000011fbe2f47 -[GlassApplication runLoop:] + 1783
28 com.apple.Foundation 0x00007fff99e9275e __NSThreadPerformPerform + 229
29 com.apple.CoreFoundation 0x00007fff907ea5b1 __CFRUNLOOP_IS_CALLING_OUT_TO_A_SOURCE0_PERFORM_FUNCTION__ + 17
30 com.apple.CoreFoundation 0x00007fff907dbc62 __CFRunLoopDoSources0 + 242
31 com.apple.CoreFoundation 0x00007fff907db3ef __CFRunLoopRun + 831
32 com.apple.CoreFoundation 0x00007fff907dae75 CFRunLoopRunSpecific + 309
33 libjli.dylib 0x0000000101f3591c CreateExecutionEnvironment + 871
34 libjli.dylib 0x0000000101f316a8 JLI_Launch + 1952
35 libpackager.dylib 0x0000000101efcf28 JavaVirtualMachine::StartJVM() + 3224
36 libpackager.dylib 0x0000000101f032b3 start_launcher + 115
37 com.app.Application 0x0000000101e7bcc8 main + 248
38 com.app.Application 0x0000000101e7bbc4 start + 52

We have seen this also in other system configurations.
We are not changing the scene in the stage, but we are showing a 2nd stage and hiding the first one.
Sometimes the user is able to click on the second stage, sometimes it crashes before any user input.
It seems to be independent of the second stage content, since we can show two different stages as our second stage and we have seen this crash while showing any of the two.