Motorola's desktop Connect software and Android app received a significant update today, adding support for a host of MMS features previously not available. Most importantly, Motorola Connect can now actually display MMS messages, be they picture messages or group messages. You can also respond to such messages now through Connect, though only using the SMS protocol. That means you can't send pictures from Connect, and you can't send group messages, either (replies will only be sent to the original sender).
Version 1.5 also improves contact matching and phone number formatting, and there's a new permission for coarse location so Connect can identify your country code.
The updated Android app is available on the Play Store now, and the Chrome extension should update automatically.