Looking at the rules for armor check penalties, I'm a little confused as to what all is affected when you are nonproficient with armor. Is there anything beside the obvious penalties — attack rolls, skill checks, and ability checks — that being nonproficient with armor also applies to?
For example, does the penalty apply to reflex saving throws and combat maneuvers?
Let's see what the rules actually say
Nonproficient with Armor Worn: A character who wears armor and/or uses a shield with which he is not proficient takes the armor's (and/or shield's) armor check penalty on attack rolls as well as on all Dexterity- and Strength-based ability and skill checks. The penalty for nonproficiency with armor stacks with the penalty for shields.
Looks like it's pretty much what you said as "the obvious penalties". Pathfinder does not have unwritten rules that would imply the rest. It only does what it says it does. So you get no other penalties other than what's printed. Specifically to your question, you don't get a reflex save penalty.
As Wyrmwood pointed out below, you would get a CMB penalty as combat maneuvers are attacks and penalties to attack apply to your combat maneuvers, also. Quote below taken from PRD -> Combat -> Combat Maneuvers.
Combat maneuvers are attack rolls, so you must roll for concealment and take any other penalties that would normally apply to an attack roll.
