There is uncertainty in measuring the position and momentum of a particle simultaneously and to arbitrary precision and this is expressed by the famous Heisenberg uncertainty principle. This is a true fact but the amazing thing is that this uncertainty does not arise from practical limitations of the measuring device. Actually, at the deepest level, the uncertainty principle has nothing to do with taking measurements. It is a law of nature!
Forget about momentum, even the position of a particle cannot be specified precisely. If I understand correctly, the position of the particle you measure might be different from what I measure (even if you and I measure with same device which can measure with arbitrary precision ). In a mathematical sense, the position of this particle is actually a probability distribution. The act of observing is the most crucial and provides with an instantiation of the position. These instantiations, of course, need not be the same.
It was startling for me when this whole new interpretation sinked in. Such an interpretation has many philosophical implications as well but it is best not to go down that lane. This rambling is a result of two videos I watched today :-
2) The amazing series of lectures by Prof.V.Balakrishnan (balki), at IITM on youtube, http://www.youtube.com/watch?v=TcmGYe39XG0&feature=PlayList&p=0F530F3BAF8C6FCC&index=0