Based on advice from #ubuntu-mozillateam, I found and ran the test suite; here's the output

Running TestVersionComparator tests
All comparisons OK
../../dist/bin/run-mozilla.sh ../../dist/bin/test_all.sh ../../dist/bin/test_xpcom
../../dist/bin/test_xpcom/test_storagestream.js: PASS

../../dist/bin/run-mozilla.sh ../../dist/bin/necko_unit_tests/test_all.sh
../../dist/bin/necko_unit_tests/test_bug331825.js: FAIL (see ../../dist/bin/necko_unit_tests/test_bug331825.js.log)
../../dist/bin/necko_unit_tests/test_bug336501.js: PASS
../../dist/bin/necko_unit_tests/test_content_sniffer.js: FAIL (see ../../dist/bin/necko_unit_tests/test_content_sniffer.js.log)
../../dist/bin/necko_unit_tests/test_cookie_header.js: FAIL (see ../../dist/bin/necko_unit_tests/test_cookie_header.js.log)
../../dist/bin/necko_unit_tests/test_event_sink.js: FAIL (see ../../dist/bin/necko_unit_tests/test_event_sink.js.log)
../../dist/bin/necko_unit_tests/test_http_headers.js: FAIL (see ../../dist/bin/necko_unit_tests/test_http_headers.js.log)
../../dist/bin/necko_unit_tests/test_parse_content_type.js: PASS
../../dist/bin/necko_unit_tests/test_protocolproxyservice.js: FAIL (see ../../dist/bin/necko_unit_tests/test_protocolproxyservice.js.log)


Oh no!  ../../dist/bin/necko_unit_tests/test_all.sh just dumped a core file.

Here're the log files:
mcasadevall@dawn:~/src/thunderbird-2.0.0.22+build1+nobinonly/build-tree/mozilla/dist/bin/necko_unit_tests$ cat *.log
nsNativeComponentLoader: autoregistering begins.
nsNativeComponentLoader: autoregistering succeeded
nsNativeComponentLoader: registering deferred (0)
WARNING: NS_ENSURE_TRUE(NS_SUCCEEDED(rv)) failed, file nsStringBundle.cpp, line 273
pldhash: for the table at address 0xf7588, the given entrySize of 44 probably favors chaining over double hashing.
###!!! ASSERTION: no native to utf-16 converter: 'gNativeToUnicode != INVALID_ICONV_T', file nsNativeCharsetUtils.cpp, line 374
Break: at file nsNativeCharsetUtils.cpp, line 374
###!!! ASSERTION: no utf-16 to native converter: 'gUnicodeToNative != INVALID_ICONV_T', file nsNativeCharsetUtils.cpp, line 375
Break: at file nsNativeCharsetUtils.cpp, line 375
Segmentation fault (core dumped)
nsNativeComponentLoader: autoregistering begins.
nsNativeComponentLoader: autoregistering succeeded
nsNativeComponentLoader: registering deferred (0)
WARNING: nsExceptionService ignoring thread destruction after shutdown, file nsExceptionService.cpp, line 191
WARNING: No event queue listener?, file nsEventQueue.cpp, line 79
Type Manifest File: /home/mcasadevall/src/thunderbird-2.0.0.22+build1+nobinonly/build-tree/mozilla/dist/bin/components/xpti.dat
*** test pending
*** test finished
*** exiting
*** PASS ***
nsStringStats
 => mAllocCount:           1406
 => mReallocCount:          977
 => mFreeCount:            1406
 => mShareCount:           1706
 => mAdoptCount:            181
 => mAdoptFreeCount:        180  --  LEAKED 1 !!!
nsNativeComponentLoader: autoregistering begins.
nsNativeComponentLoader: autoregistering succeeded
nsNativeComponentLoader: registering deferred (0)
WARNING: NS_ENSURE_TRUE(NS_SUCCEEDED(rv)) failed, file nsStringBundle.cpp, line 273
pldhash: for the table at address 0xfe2c8, the given entrySize of 44 probably favors chaining over double hashing.
###!!! ASSERTION: no native to utf-16 converter: 'gNativeToUnicode != INVALID_ICONV_T', file nsNativeCharsetUtils.cpp, line 374
Break: at file nsNativeCharsetUtils.cpp, line 374
###!!! ASSERTION: no utf-16 to native converter: 'gUnicodeToNative != INVALID_ICONV_T', file nsNativeCharsetUtils.cpp, line 375
Break: at file nsNativeCharsetUtils.cpp, line 375
Segmentation fault (core dumped)
nsNativeComponentLoader: autoregistering begins.
nsNativeComponentLoader: autoregistering succeeded
nsNativeComponentLoader: registering deferred (0)
WARNING: NS_ENSURE_TRUE(NS_SUCCEEDED(rv)) failed, file nsStringBundle.cpp, line 273
pldhash: for the table at address 0xf8290, the given entrySize of 44 probably favors chaining over double hashing.
###!!! ASSERTION: no native to utf-16 converter: 'gNativeToUnicode != INVALID_ICONV_T', file nsNativeCharsetUtils.cpp, line 374
Break: at file nsNativeCharsetUtils.cpp, line 374
###!!! ASSERTION: no utf-16 to native converter: 'gUnicodeToNative != INVALID_ICONV_T', file nsNativeCharsetUtils.cpp, line 375
Break: at file nsNativeCharsetUtils.cpp, line 375
Segmentation fault (core dumped)
nsNativeComponentLoader: autoregistering begins.
nsNativeComponentLoader: autoregistering succeeded
nsNativeComponentLoader: registering deferred (0)
WARNING: NS_ENSURE_TRUE(NS_SUCCEEDED(rv)) failed, file nsStringBundle.cpp, line 273
pldhash: for the table at address 0xfe4f8, the given entrySize of 44 probably favors chaining over double hashing.
###!!! ASSERTION: no native to utf-16 converter: 'gNativeToUnicode != INVALID_ICONV_T', file nsNativeCharsetUtils.cpp, line 374
Break: at file nsNativeCharsetUtils.cpp, line 374
###!!! ASSERTION: no utf-16 to native converter: 'gUnicodeToNative != INVALID_ICONV_T', file nsNativeCharsetUtils.cpp, line 375
Break: at file nsNativeCharsetUtils.cpp, line 375
Segmentation fault (core dumped)
nsNativeComponentLoader: autoregistering begins.
nsNativeComponentLoader: autoregistering succeeded
nsNativeComponentLoader: registering deferred (0)
WARNING: NS_ENSURE_TRUE(NS_SUCCEEDED(rv)) failed, file nsStringBundle.cpp, line 273
pldhash: for the table at address 0xf7a70, the given entrySize of 44 probably favors chaining over double hashing.
###!!! ASSERTION: no native to utf-16 converter: 'gNativeToUnicode != INVALID_ICONV_T', file nsNativeCharsetUtils.cpp, line 374
Break: at file nsNativeCharsetUtils.cpp, line 374
###!!! ASSERTION: no utf-16 to native converter: 'gUnicodeToNative != INVALID_ICONV_T', file nsNativeCharsetUtils.cpp, line 375
Break: at file nsNativeCharsetUtils.cpp, line 375
Segmentation fault (core dumped)
nsNativeComponentLoader: autoregistering begins.
nsNativeComponentLoader: autoregistering succeeded
nsNativeComponentLoader: registering deferred (0)
WARNING: nsExceptionService ignoring thread destruction after shutdown, file nsExceptionService.cpp, line 191
WARNING: No event queue listener?, file nsEventQueue.cpp, line 79
Type Manifest File: /home/mcasadevall/src/thunderbird-2.0.0.22+build1+nobinonly/build-tree/mozilla/dist/bin/components/xpti.dat
*** test pending
*** test finished
*** exiting
*** PASS ***
nsStringStats
 => mAllocCount:           1508
 => mReallocCount:          979
 => mFreeCount:            1508
 => mShareCount:           1703
 => mAdoptCount:            181
 => mAdoptFreeCount:        180  --  LEAKED 1 !!!
nsNativeComponentLoader: autoregistering begins.
nsNativeComponentLoader: autoregistering succeeded
nsNativeComponentLoader: registering deferred (0)
WARNING: NS_ENSURE_TRUE(NS_SUCCEEDED(rv)) failed, file nsStringBundle.cpp, line 273
pldhash: for the table at address 0x100f60, the given entrySize of 44 probably favors chaining over double hashing.
###!!! ASSERTION: no native to utf-16 converter: 'gNativeToUnicode != INVALID_ICONV_T', file nsNativeCharsetUtils.cpp, line 374
Break: at file nsNativeCharsetUtils.cpp, line 374
###!!! ASSERTION: no utf-16 to native converter: 'gUnicodeToNative != INVALID_ICONV_T', file nsNativeCharsetUtils.cpp, line 375
Break: at file nsNativeCharsetUtils.cpp, line 375
Segmentation fault (core dumped)