With oversampling and DSP dynamic range should not be much of a problem these days. It is now up to 22 bits, which would be a dynamic range of ca 2 million to one.
My experience with trying to do trace analysis with NMR is that the diffuculty is the complexity of the NMR spectrum. Things like 13C satellite peaks and impurities in the NMR solvent only compound the problem. Another reason that trace analysis has not become too popular is that there are other far cheaper methods. For example, GC/MS, LC/MS, etc. I don't know how many times I have had to try to convince people (usually from other departments) that what they really want is a separation method, not NMR.

The following references might be relevant.

1. Separation and Analysis of Trace Degradants in a Pharmaceutical Formulation Using On-Line Capillary Isotachophoresis-NMR. Stacie L. Eldridge, Valentino K. Almeida, Albert K. Korir, and Cynthia K. Larive. Anal. Chem., 2007, 79 (22), pp 8446–8453

2. NMR spectroscopy in pharmaceutical analysis. By Iwona Wawer, Ulrike Holzgrabe, Bernd Diehl ...discuss possibilities for use of NMR for detection of impurities in pharmaceuticals.

3. Analytical techniques for biopharmaceutical development (pages 311-318) By Roberto Rodríguez-Díaz, Tim Wehr, Stephen F. Tuck Publisher CRC Press, 2005 ISBN 0824707060, 9780824707064

They write "...Detecting a low level-level (<10ug/ml) small molecule impurity in the presence of active protein and excipients at much higher concentrations is a daunting analytical problem. In many cases, NMR is an excellent method for solving such challenging analytical problems..."

I do agree with Kirk Marat that, in most cases, other techniques would be preferable.
However, for specific cases, such as those discussed above, NMR may have some advantages.

You definitely can use an internal standard at specific concentration and use ratios of peak integrals to measure concentrations by NMR, but one thing to be mindful about is distortion of peak intensity by saturation - i.e. pulsing too frequently and thereby not allowing for sufficient relaxation of magnetization between scans.

A book "High-Resolution NMR Techniques in Organic Chemistry" (ISBN 978-0-08-042798-0) by Timothy Claridge has a very good explanation of this experimental detail in Chapter 4

So - yes it must be possible to set upper limit of impurity content using NMR data, the lowest number that can be reported this way depends on sensitivity of the instrument and amount of sample in the tube or rotor (for solids).

I hope that somebody will correct me if I'm wrong.