Now we get into the nitty gritty of the combat system, what makes it tick, what we want to keep and what we want to get rid of.
Initiative and Actions
Nothing is wrong with the initiative system as written. The main change that is going to come here is from the movement to a d10/percentile system.
Clarity and intuitiveness is a goal as well. I've heard stories of things going horribly awry due to misunderstandings of the rules. In one story, each player takes all of their actions at once, so Player 1 takes their 3-5 attacks, then Player 2 attacks 3-5 times, etc. until the last player in the initiative gets so mad at having to wait so long and having most of the enemies defeated already that he uses his 3-5 actions to attack the other PCs!
Probably the simplest way to set up an initiative order is to make a die roll and add it to an attribute (probably whatever I use to represent speed). 1 or 2d10 for granularity and interest. Not too much more or randomness will overwhelm character ability. I definitely want character ability to matter much more than it does in the current iteration of Rifts.
One possible solution to the action situation is to implement "initiative passes." I saw this in at least one version of Shadowrun. Initiative is rolled and everyone takes one action in initiative order. Then 10 is subtracted from everyone's initiative and anyone who still have an initiative above 0 can act again. This cycle continues until no one has a positive initiative total anymore. Then initiative is rerolled for the next round.
Another option is "tick-based" initiative, which has notably appeared in the second edition of Exalted and the Feng Shui RPG. Every action that a character has a cost which generally reflects how long the action takes to complete. Small quick actions may be taken multiple times while another character who takes more involved actions must wait much longer until they can act again.
I'm not firmly decided on which option to use quite yet.
One thing that definitely needs clearing up is combat movement. In Rifts, movement is governed by the Speed attribute, but it is not well explained. There is a table detailing running speed in miles and kilometers per hour, but no real explanation of how it governs movement over a combat round. While some gamers are content to play out battles using only their imaginations, or simple sketch-maps, there are those who cry for the minis and gridded battle mat when fights break out.
Also very important, it should work for both descriptive combat and gridded combat. One thing that I hated about Savage Worlds is their use of the "Savage Worlds inch." You are assumed to be mapping everything out, so all measurements are given in inches (representing 1 inch on the tabletop). This wouldn't be so bad, but this "inch" translates into two yards. Meaning that when my players asked about distances, I had to take the time to convert 1 inch into 2 yards. Usually just a doubling or a halving, depending on which way the conversion was going, but it still took away from my valuable game time. D&D's 5 foot square or GURPS' 1 yard hexes are far more intuitive.
Attack and Defense
Now we get into the actual dice rolling. Combat will be resolved with percentile rolls, just like every other die roll in the system. Attack and defense will be a pair of "blackjack" rolls (roll as high as you can as long as it's below your skill %). So if the attack is successful with a result of 48, the defender must roll higher than 48 but less than their defending skill % in order to avoid the attack.
This does a pretty good job of mapping the Palladium combat dice flow to a percentile system. It will also serve as a model for opposed actions outside of combat, a mechanic that Palladium has been sorely lacking. The recent addition of the Perception roll makes this all the more obvious. Especially since the rolls it opposes are percentile rolls (like Prowl) and the Perception check is made on a d20.