Junk made it into my keg

I just brewed an all grain Fuller's ESB clone, which I racked to a corny this evening. I now realize that I need to refine my process of straining from the kettle to the carboy. I had a lot of trub at the bottom of the carboy and there were loose hops floating about. Well, I had a lot of difficulty racking to the keg. I use an orange carboy cap and push with CO2. I neglected to use one of those orange caps at the end of my racking cane. Every few minutes I had hop flowers plugging the racking cane. Unfortunately, I had a bit of splashing in the keg. Anyhow, my main concern now is how to deal with the hop remains in the keg. I would think that they will clog the beverage tube once it's carbonated and dispensed.
Any ideas on how I can prevent clogging?
And what is a good way to avoid this problem in the future?

Thanks!

I never strain or filter anything. I don't need to. I use a fining agent 15 minutes before the end of the boil and it all falls to the bottom. If you ferment and condition in the primary for 10 to 14 days all the crud will be on the bottom. Use the autosiphon or a racking cane with the orange thingy on the bottom and you will have no problem. I never use whole hops for the reason you mentioned and get great hop flavor. I do not see why people use them, as I see no change in the final outcome.

The homebrew shop only had whole hop Goldings, no pellets. Re: the orange racking cane cap -- I absentmindedly forgot it. After 8 years or so of not brewing, this is my 2nd batch back...fortunately, I made fewer mistakes than on the previous batch, though...so that's progress

I've dry hopped my last couple of batches in my secondary, and the first time didn't have a great way of getting the hops out when it came to bottling time.

However, I have a big grain bag I bought to do partial mashes, before I switched to all grain. I was thinking I would sterilize it, and then put it in my bottling bucket and transfer my beer over the top of it. That way I wouldn't be splashing my beer through a filter, and then when I was done I could just pull the bag out of the bucket, collecting all the large chunks(mainly hop leaves).

Not sure if that would work for you with kegging, but it's what Im going to try.