I am considering picking up a 2013 rdx with approx 112,000 miles on the clock; is there anything I should watch out for in particular with these such as burning excess oil or anything of that nature?

 

Service records will save you a lot if you can get them in detail. I purchased a 2013 RDX @ 110k miles or so without detailed service records and ended up having to do the 100k mile service just to be safe and that cost me an extra $1900 for B12345 service + resealing a leaking oil pump.

 

Indeed it is due for a timing belt service. That would include the belt, tensioner, idler, water pump, drive belt, coolant (Honda long life only) and spark plugs. NGK specified ones, not just anything.
The timing belt compoinents should be OEM or there is a kit to be had from someplace like Rock Auto made by Aisin that is as good a quality as OEM. (Aisin may make the parts for Honda)

Honda/Acura products rarely burn oil. They sometimes leak it. There have been some engines that used low friction piston rings that actually burned oil. Those were not used in the RDX V6.

There is a device you can plug into the coolant sensor that keeps the VCM from operating. This can help these engines last longer and help save very expensive active engine mounts. See
threads here on Google Muzzler. Only install on a cold engine.

 

I purchased a 13 RDX-Tech AWD with just short of 55k miles for the wife in February 2018. Her RDX has not and does not consume any perceptible amount of oil...her RDX is currently knocking of door of 100k miles. It has also had an S-VCM controller installed since around week 2 after purchase, so it's been running on all 6 cylinders all the time since our ownership.

Regardless of the reason...yes, there are more than a few Honda/Acura models which either have a reputation for consuming oil -or- Honda/Acura has issued recalls to remedy excessive oil consumption. My wife's previous (VCM equipped) 08 Odyssey and 11 Pilot consumed oil...if you take a look over in the TL or MDX forums you read about the 3.7L engines consuming major oil and Honda has been forced to recall an uncomfortable number of those models for major engine work. Engine oil consumption has also been a complaint of many 2 Gen TSX models and same goes for early years of the 8th Gen Accord models...both with the 2.4L engine.

Again...oil consumption doesn't seem to be an issue with maintained 2nd Gen RDXs and certainly not in my specific case. I service my wife's RDX when the MID indicates it's time to do so...with Valvoline 0-20w full Synthetic...same as I do with the rest of my personal Honda/Acura "fleet."

An issue which was very noticeable with wife's RDX after purchase was the very unsettled, jerking and juddering transmission. It drove like a pig going up thru the gears and shifting in and out of eco mode was very noticeable on the highway. After performing a 3x Drain/Fill with MaxLife synthetic ATF and installing the S-VCM Controller...the wife's RDX settled into rewarding the refined driving experience a small 270 horse premium SUV should.