I'm interested in buying a young bitch for my dog as a companion for life but the pedigree papers show that my dog and the bitchs sire (dad) are half brothers, both sharing the same dad. This would make my dog the interested bitch's half uncle.
Would this cause a problem in anyway in regards of breeding and registration? 

The Kennel club will not register father/daughter,  brother/sister, or mother/son matings,  half uncle they would register.

Although depending on breed it is always good to widen that gene pool, unless it is genetically better for the breed in breeding in or out breed standard/health/temperament issues.

But, with regards to registration it would be allowed. :-)

So you are looking for a bitch to breed with your young dog?

Although registering puppies from this combination would be permissible, it is not a mating that I would do UNLESS I actually knew a lot about the dog that they have in common - temperament, health, longevity etc. And - just as an aside - I would only do a combination once, as I can't see any point at all in repeating matings, unless you haven't got the sex of puppy that you wanted from the combination.

Half Uncle to niece has been my favourite mating, one of my champion bitches  is from such a mating, as was her RCC winning mother. 

Her champion daughter is from an outcross mating, but my third champion, her daughter is,  by her maternal half brother on their champion Dam, though bother the sires are imports from different continents.