There are several facets to this question:
From the technical point of view, answering the "How ?"
There are several technologies to master plus a number of "nice to have".
Number one is Java. The Android SDK is based on the assumption that all apps are written in Java. Although arguably there are some emerging third party solutions to develop in .net (see monodroid), after all, the underlying OS is Linux.
The second is eclipse. Although there are a number of 3rd Party SDKs around, some betters than ADT, on Intellij, or on Netbeans, Google's efforts are officially focused only on eclipse for now.
Edit : As of Jan 2016 Google is officially supporting Android Studio as its official IDE.
In the android architecture, there a number of building blocks for which a little bit of exposure will always be helpful:
SQLite
General notions of video and audio streaming, codecs. For OpenCore (android.media).
OpenGL drawing.
REST based Web services, XML or JSON.
Notions pertaining to the ARM architecture for Native Code development.
Plus, reading in my crystal bowl, Android developers should also know their Linux and be proficient in native languages for the day when Google ditches Java and substitutes it with go or some other stuff they might have brewing somewhere (see their "Native Client" initiative in the browser domain). Google have already release a NDK (Native Development Kit) for c and C++ using standard JNI mechanism to complement Dalvik.
From the commercial point of view, answering the "What ?".
Android developers should be Android users themselves of course. However, not just standard mobile phones users but also tablet users. They should actually adopt a Jobsian attitude - always asking themselves "How could I do that better with my phone, my tablet or any not-yet-on-the-market-consumer-electronics-appliance ?".
There are plenty of android application that have no market leader yet, not necessarily related to mobility (or the usual boring "where-is-the-nearest- pizza ?" app). Here are a few ones I can't get out of my mind personally (until I have more time ;-).
teach your kid to draw and read.
flashcards to learn foreign languages.
UK-FreeSat TV-guide + remote control.
yours here (cuisine recipes... etc).