Hello Brian. You cannot check oil with engine running, period! The easiest way to check oil is after sitting overnight, you will see a definite line where oil level is. Of course you can pull and wipe dipstick to check oil.
Smoke coming out dipstick tube is not that unusual.
No PCV valve? A 67 should have one.
As engine ages with miles and rings wear more and more blowby will appear. An ordinary engine with PCV working correctly, you will not see any blowby. After shutting engine off and pulling dipstick you may see wisp of oil vapor
 

Briangillen wrote:

I've got a 1967 Mustang 289.I took the car out today for a test drive and while it was still running I checked the oil and smoke started coming out of the dipstick tube.

I googled it and it appears that the PCV valve is a common cause of this; when I got the car it didn't have a PCV valve so I added one. I think it's the correct one. Not sure What to do or how to check it.

I don't want to blow out any seals or anything anybody have any tips.

You mention that you added one.  Can you elaborate on how you added one?
http://www.aa1car.com/library/pcv.gif


Easy to test the valve.  IF you suck on the valve, it should only let you suck air in one side only. 

Briangillen wrote:

The car came to me with aftermarket valve covers that had a breather on it. I just replaced the breather with a rubber grommet that holds the pcv valve and ran the line to the carb.

Well, its a circular system,  Air needs to come in one valve cover,  and air is sucked out the other valve cover.
You might be missing a hose on the opposite side valve cover

Is the valve with the correct end pointing toward the carb? 

Do you have it hooked up to the correct vacuum source type?
 

 

Briangillen wrote:

The pcv goes to the base of the carb, but the other side is just capped. Should that be changed to some sort of breather? You can kinda see in the photo.

Yeah it shouldn't be capped.  It should have either a vented cap so air can be sucked into the cap or a cap with a hose that goes to the air cleaner so clean filtered air can be sucked into the hose leading to the crankcase.  Its about keeping pressure even in the crankcase so while the engine is producing vacuum and sucking in vapors on the one side with the pcv valve basically expelling the gases in the crankcase,  the other side is letting clean air into the crankcase.  Kinda like inhale and exhale.  Crankcase inhales good clean filtered air thru one valve cover, and exhales it out the other valve cover with the pcv valve.  
 

Briangillen wrote:

Good to know.  Just went out to the garage on put the breather cap on the other side.  No where to connect it to the air filter, but it will have to do. I'll try it tomorrow and see if I can see any difference.  Thanks for your help MarkinSC!

I didn't see your air filter/air breather in that pic.  Just the carb. Hopefully the other valve cover has a hole already in it.  So you just have to add a hose to the air filter.  OR they have the breather caps without the hose nipple.  Those breather caps have a filter built into the cap.So you could just add one of those into that valve cover.

PLease discount double check that pcv valve and make sure the correct end is pointing toward the carb. If you pull the pcv valve out of the valve cover with the hose still attached to it leading to the carb,  it should be sucking air in the end that you just pulled out of the valve cover. You should be able to stick your thumb over the valve and feel it sucking on your thumb. You also might notice engine stumble cause you just created a vacuum leak. When you put your thumb over the valve the vacuum leak is stopped and engine shouldn't run rough then.
 

Makeing it an "open system" would be a lot easier. Hole saw a hole in the VC and put a vented oil filler cap on.
BTW.......where do you add oil when needed?
6sal6

Briangillen wrote:

Hi guys - checked the pcv valve and it's has lots of suction, so I think that's good. The other side now has one of those breathers like markinsc posted. Id taken one off to add the pcv valve. 6sally6 the side without the pcv used to just have a cap, that's where I've been putting the oil. The breather is in that spot now but it just slides in (pretty snugly) so it should still be okay to use to add oil. Thanks to everyone! Brian

that valve shouldn't let any suction go in the opposite direction. My fault for not providing testing instructions for that. Its a "one way" valve. The spring inside it is supposed to prevent suction in the opposite direction. In other words,  air shouldn't be traveling in the direction from the carb toward the pcv valve and then into the crankcase, if so this incoming air will possibly try to come out the dipstick tube or the newly installed breather cap. 

Did adding the breather cap on the other side solve your issue?  Do you still have smoke coming out your dipstick?
 

All of that said, the engine crankcase would have had a vacuum pulled on it by the PCV valve and the open dipstick tube would have been an INLET of fresh air, not a smoke outlet.  While all the previous advice was spot-on as to how a PCV valve should be connected, I don't think it has much to do with smoke coming OUT of the dipstick tube.  In my opinion, that would be coming from excessive blowby.

A compression test would be in order, or just monitor the oil level after the PCV valve correction is completed to see if it uses oil.