Same problem in a different thread: http://arduino.cc/forum/index.php?topic=130161.0
The solution there fixed this problem for me too.

I am going to try the same thing. Franky47 is making updates to his awesome MIDI library that allows multiple instances, one on each serial port.
https://github.com/FortySevenEffects/arduino_midi_library/tree/release/4.0

I haven't started yet.
I don't mind keeping the Arduino inside the project. I'm not mass-producing anything and I can take the project box apart easily enough.
I'm going to use an old KVM switch - the type for the ancient AT keyboards, since they have the same DIN sockets as MIDI.

my plan was just to use the Arduino Mega; it has three serial ports.

The Halloween Pumpkin project at Adafruit has almost every element you require.
http://www.ladyada.net/make/pumpkin/pumpkin.html

If you can read French (I can't), follow this
http://arduino.cc/forum/index.php/topic,64900.0.html
it looks like a porting of the MrMidi you posted above to Arduino. I tried to get it working but it's far too complicated for me. I would rather start from scratch and use the new SD card libraries and Arduino 1.0.

Even an Uno can do a decent job with sequencing beatbox kind of stuff.

Do you have another MIDI keyboard to try? I mention it because I was building a MIDI circuit too, and with a Yamaha PSR keyboard it would always seem to drop notes, and even add notes!! And I must have gone through my schematic and circuits a hundred times.
But then I plugged into my Kurzweil piano and it worked flawlessly... and just to be sure I have a Rockband controller which has MIDI out, and it works fine as well... So I believe these Yamaha PSR keyboards don't follow the standards too well.

I have been looking for the same thing. But so far this hasn't been done specifically for Arduino that I can find. There are projects that let you convert MusicXML or .MID files on your PC, and then include the conversion in your Arduino sketch.
http://www.adebenham.com/2010/02/musicxmlmidi-for-arduino/
http://code.google.com/p/miditones/

Solved.
A tip from the author of the MIDI schematic I used (at http://www.thebox.myzen.co.uk/Hardware/MIDI_Shield.html ) led me to tie a pullup resistor to RX (10k between +5V and pin 0).
Many, many thanks to him!
\\'9

You don't need to refresh the entire grid each time!
Just change the specific LED that relates to the MIDI note. The 7219 will take care of the rest.

If you want to continue to use the MIDI library, you can simplify your code a lot by using the event handlers. To do that, in your setup function:

Code:

  // Initiate MIDI communications, listen to all channels, turn off thru mode
  MIDI.begin(MIDI_CHANNEL_OMNI);
  // By default, the MIDI library sends everything THRU. We do NOT want that!
  MIDI.turnThruOff();

  // Connect MIDI status changes involving a channel to handlers
  MIDI.setHandleNoteOn(HandleNoteOn);
  MIDI.setHandleNoteOff(HandleNoteOff);

Then, create a function for handling note on and note off:

Code:

void HandleNoteOn(byte channel, byte pitch, byte velocity) {
 // check your pitch, velocity, and channel here
 // turn on the LED matching pitch
}
void HandleNoteOff(byte channel, byte pitch, byte velocity) {
 // check your pitch, velocity, and channel here
  // turn off the LED matching pitch
}

Now your loop function is simple:

Code:

void loop() {
   MIDI.read();
}

Thank you Keith for putting this project on Kickstarter. It is something I have been dreaming about (even studied the SAM2195) but it's way beyond my skills. For now I'm sticking to simpler MIDI projects.

I got a BoArduino (adafruit.com/products/72) to use in a MIDI project I am doing. I have the project almost working but the BoArduino is acting very strangely.
When the FTDI Friend is plugged in, the code runs flawlessly (with or without the external power supply, but setting the jumper accordingly and all the grounds are tied together). But when I unplug the FTDI the code runs erratically.
Without the FTDI friend, the box starts dropping messages and garbage starts appearing on the LCD. MIDI messages are dropped. For example I start to get a lot of "stuck" notes, notes that don't play at all, and even a random note once in awhile that I didn't play!
I used a 9V power supply and have tried other power supplies. The jumper is set to ext only when the power supply is plugged in. Other test code I run on the BoArduino seems to be OK (blink sketches etc.) without the FTDI, so I think the BoArduino is put together correctly.
The link below is to a picture of the display. The bargraph at the bottom (and the red LED) should only show when a note is on; here I have no hands on the keyboard. http://flic.kr/p/aXfksM
I'm wondering do I need to wire something up to mimic something the FTDI is providing? Can BoArduino even do serial in/out without it?
The project has MIDI in/out, a 20x4 LCD (ID: 198) and a rotary encoder. The code and schematic is here: https://github.com/mymaestro/Arduino-MIDI-projects/tree/master/midiTranslator
Any ideas what could be going on?

Well, the main difference between Duemilanove and Uno is the USB interface, so it's not surprising that a serial interface doesn't continue to act in the same way. http://arduino.cc/en/Main/Boards
I wouldn't expect the same results from the USB interface.
Duemilanove boards are still available (and being discounted) so you should try to get some.