I just ran 4 Palladium events at OrcCon this weekend (Mechanoids and Ninjas & SuperSpies) and the games were fun and easy to run and my players (mostly Palladium noobs) had a great time.
Palladium, like AD&D and many other early RPGs, really shines when you houserule them to fit your own GM style. Palladium has a strong balance mechanic - it's called the GM and the GM is expected to challenge each character and group appropriately. But Palladium was born back when Traveller, RuneQuest and AD&D ruled the earth so there are different expectations of play than modern RPGs.
Here's my three key houserules:
1) Fast and Furious
I find Palladium runs best when you run it with a comic book atmosphere and action movie sensibility by going gonzo. The core system becomes invisible in gameplay (much like OD&D and CoC) so it is important to capitalize on that and keep the game moving at very fast pace. If you bog down in rules worries, it's over.
2) Momentum of Combat
I read "Attacks per Melee" as "Actions per Round". When your Initiative comes up, you do your stuff - any movements, skill usage and attacks - and then decide how many actions you hold in reserve for defenses. You may always spend actions on defenses before your Initiative comes up, but any unused actions at the end of the round are lost and we reset all our actions for the next round. I use tokens to let people visualize and move them about like an attack / defense pool.
BTW, I give people the option to spend an action on making a called shot or just taking -3. Also, I make sure that when a specific part is hit on a vehicle, I take the same damage off the Main Body as well to keep the combat going quickly.
3) Chop that NPC in half!
I like quick, brutal combats where stuff explodes. Everything that is not a PC or PC gear gets its SDC / MDC / HP cut in half. If it was 300, it's now 150 at most and most living things are smart enough to bail when 50% of their life/defense is gone so that 300 MDC monster in the book may retreat to fight again after 75 damage in my games.