I have been having a Lord of the Rings 'marathon' and I noticed that when the Uruk'Hai have their limbs cut off they do not bleed. Was this just a production error or is there an actual reason?
There is no canonical reason for this in the books nor is there a canonical reason for this mentioned in any of the special features. I actually never noticed this, myself. Given the lack of a canonical reason for Uruk'Hai failing to spray blood when they are cut mentioned anywhere, I'm going to assert that it logically follows that this is an artifact of production. In other words, canonically this is incorrect as they should be bleeding.
It's probably a production choice, as @Martha suggests in the comments below, in order to avoid an R rating. It could be a choice to reduce costs associated with the special effect of spraying blood. It also could be a production error, but that's rather unlikely given that this was the franchise of the studio by virtue of the amount of money invested before it ever saw a theatre.
It's a requirement of a PG-13 rating: no depictions of "strong violence including blood and gore". The amount of blood and gore allowed in PG-13 versus R walks a fine line, and generally the less of the other things (sex, drugs, language) that you have, the more blood and violence is allowed. As LotR has virtually no sex or language, and the only "drug" other than alcohol (pipeweed) is ambiguous as to its effects, so they can show blood and violence for longer, but still have to toe a line with regard to graphic violence like dismemberment and beheading.
Also remember these films were released worldwide, and other countries such as China and Japan have different, often stricter regulations on what can and can't be shown with regards to violence, even while (as an aside) the same country may have reduced restrictions with regard to nudity. The U.S. often takes a reversed stance as compared to the rest of the world with regard to the amount of skin you can show versus the amount of blood. Of course, movies versus TV also differs; Weta Workshop had to go back and composite a helmet over a particular shot of an Uruk'Hai's head on a pike to avoid it being too graphic to show on U.S. network television.