When I read your post I took from it that it was blowing oil out of the pipe, but now that you posted the reply, I feel better about the engine.
I think Agvg is right. Some of the older tractors with some hours on them will smoke (mostly white) when they are first started. Once they come up to operating temperature most of them will clear up enough that you wont notice it. He is also correct in that they need to be worked to keep them running properly. Once they are at operating temp you should be able to go from idle instantly to 75% to 80% throttle with just a brief puff of black smoke till the engine catches up with the injector pump. So a little black smoke under a brief load is somewhat normal. If its a constant heavy smoke, some changes to your settings need to be made, whether its a gear change or a lighter depth of cut on your implement.
How many hours does the hour meter show?
As for the lifters being different heights, that is normal, depending on the position of the cam lobe. So when you tore the engine apart and found the lifter raised higher than the other, that would be raising the push rod, pushing on the rocker arm, making that valve open. That is why some rocker arms feel tight when you wiggle them. If they do wiggle a small bit, that actually is normal is the valves are set properly.
When your piston come to TDC (top dead center) on the compression stroke (firing), you can and should be able to wiggle both the intake and exhaust rockers on that cylinder since you dont want any down pressure on the springs because you want the valves completely closes at that very moment.
Chances are there is nothing wrong with the motor or the internals, but since its apart, check your valve guides and if you find nothing wrong with them, lap the valves in and put it back together.
Take your injectors and have them tested and check the spray pattern of the nozzles and make sure that chatter with a mist of diesel versus just spraying out a solid stream of it. This will cause some of the smoking issues. You probably need new nozzles if they have never been changed out. Make sure that they look up the two letter code on the injector and set the pressure correctly on them.
For instance I just recently did a set of injectors that had a tag attached under the bottom of the two caps that read A N . So I look up A N for that motor and it tells me working pressure and setting pressure. Working pressure was 2500 psi but the setting pressure is 2600 psi. So they will remove the top cap, loosen the bottom one which is actually a jam nut for the adjuster. They perform a test on all of them and adjust them accordingly to the pressure results.
Be sure to install new sealing washer on the bottom of the injector make sure you have all 4 of the old ones in your hand and that you didnt leave one down in the injector hole or the new one will not seat against the old one and it will not let you injector protrude down into the head where its supposed to be.
Also new crush washers for the return line and the banjo bolts that hold it down. Do not overtighten them, they will break.