Pro Multiplatform support
Code can be ported to mobile (iOS is in the works) and other Android supported devices with minor changes to the code (just change some implementations that vary on the platform such as inputs and user interface). It can even run on certain Raspberry Pi devices.
Pro Free and open-source
jMonkey is completely free, meaning it's possible to develop and release a game with no fees or royalties. Because it is open-source, jMonkey has plenty of people fixing bugs and, adding to the engine as well as creating a variety of plugins that can be used in the engine.
Pro Java is a great development platform
Java is a well-optimized just-in-time compiled language. It's faster than languages without an effective native-code compiler such as Python or Ruby, similar in speed to other just-in-time compiled languages such as C#, while slightly slower than compiled languages such as C or C++ (with some low-level and numeric benchmarks being similar to C++).
Java also has a wide variety of high-class IDEs available.
Con Not an engine for total beginners
While it's clear that you need to know Java first before using this engine, it is recommended that you have some programming experience as well. Most performance issues and memory leaks are more due to bad programming practices than the engine itself.