Right after the replay, BitShares encountered an exception. I relaunched it and got another:
Process:               BitShares [4396]
Path:                  /Applications/BitShares.app/Contents/MacOS/BitShares
Identifier:            org.bitshares.BitShares
Version:               .. (..)
Code Type:             X86-64 (Native)
Parent Process:        ??? [1]
Responsible:           BitShares [4396]
Date/Time:             2015-04-20 21:30:07.859 -0500
OS Version:            Mac OS X 10.10.2
Report Version:        11
Crashed Thread:        0  Dispatch queue: com.apple.main-thread
Exception Type:        EXC_BAD_ACCESS (SIGSEGV)
Exception Codes:       KERN_INVALID_ADDRESS at 0x0000000000000058
VM Regions Near 0x58:
--> 
    __TEXT                 00000001040b4000-0000000105ed6000 [ 30.1M] r-x/rwx SM=COW  /Applications/BitShares.app/Contents/MacOS/BitShares
Thread 0 Crashed:: Dispatch queue: com.apple.main-thread
0   org.qt-project.QtCore         	0x0000000109e6fc3e QMetaObject::activate(QObject*, int, int, void**) + 62
1   org.qt-project.QtNetwork      	0x0000000109b4e2cc QNetworkReply::downloadProgress(long long, long long) + 76
2   org.qt-project.QtNetwork      	0x0000000109ac8770 QNetworkReplyHttpImplPrivate::replyDownloadData(QByteArray) + 1280
3   org.qt-project.QtNetwork      	0x0000000109b4ead4 QNetworkReplyHttpImpl::qt_static_metacall(QObject*, QMetaObject::Call, int, void**) + 1828
4   org.qt-project.QtCore         	0x0000000109e69393 QObject::event(QEvent*) + 755
5   org.qt-project.QtWidgets      	0x000000010686932b QApplicationPrivate::notify_helper(QObject*, QEvent*) + 251
6   org.qt-project.QtWidgets      	0x000000010686c648 QApplication::notify(QObject*, QEvent*) + 8136
7   org.bitshares.BitShares       	0x00000001040ebc6e BitSharesApp::notify(QObject*, QEvent*) + 14
8   org.qt-project.QtCore         	0x0000000109e3ea5b QCoreApplicationPrivate::sendPostedEvents(QObject*, int, QThreadData*) + 971
Now I launched it for the third time, no problems logging in! A fleeting bug of some sort. On to more testing...