Most accurate IOS app for turntable speed check

Nothing hokey about the Roadrunner.   I used my existing arm and cartridge from my previous SOTA , it is a marked improvement .

Its solid speed is why it sounds so good, I am confident of that  

Your ears, just admit, if you cannot detect that the speed is off:

IT DOESN"T MATTER!

I occasionally accidently brush against the wheel that controls my TT81's speed, and if just a speck, I don't notice, a bit more, huh, somethings wrong, oh hey, look at that number in the tiny window.

My Thorens TD124, (and my current belt drive Mitsubishi Vertical TT LT-5V) reflected dots, I would wait a few minutes for it to get naturally warm, adjust for steady, and then, if the room temp changed, say a party with lots of people, I would hear it wrong, check, sure enough the speed was off.

To a point, it only matters if you can hear it. My old ears have lost a lot of high frequency hearing. That said, I'm very aware of pith or wow. I play acoustic guitar and tuning is a constant chore, and I can always tell when a string goes off tune,

So, my trusty old Technics SL-1200 MK2 has the built in strobe that seems to work well and I've never detected any offensive pitch or speed variation.

Again, I thought the subject is how to measure speed, not how to maintain correct speed.  I agree with Elliot; it is not so important to maintain bang on 33.333 rpm as it is to maintain constant speed. I think we/I am more sensitive to speed varying during play than I am to slight errors in constant speed.  But the OP wants to measure speed per se.

Very easy to do with any laser tachometer you 

can buy online. You need some reflexive tape. Should be more accurate than an iOS app.