I have been told in many places by many people that using poultry litter to fertilize crops spreads weed seeds. However, research by Auburn, the universities of Kentucky and Georgia, and most recently, Virginia Tech found this to be untrue. The only potential avenue of poultry litter conveying weed seed occurs when the litter is contaminated during handling and storage. While many weeds seem to proliferate after litter application, objectively it is likely they are seeds already present in the soil responding to the litter as a soil amendment.
The test most often cited was conducted at Auburn University. Litter was divided into two: half was amended with a suite of weed seeds and half was not. The only weed seeds that germinated were in the half with added seeds. More recently, a group at Virginia Tech tested nine different poultry and turkey litters by mixing them with potting soil and wetting. Not a single weed germinated. In addition to this study, they also studied species composition in pastures with inorganic fertilization or poultry litter. There was no difference in plant communities based on the fertilizer source.
Where we have vulnerability is wind-aided seed accumulation on uncovered storage piles on field edges. In that case, the weed seeds you may distribute when spreading poultry litter could be your own. If you are not convinced, test your own litter samples as they did in Virginia. Or watch for weeds growing in litter storage piles that have been covered.