Pros
Qualcomm is a hotbed for learning about wireless technology being the 900lb Gorilla of CDMA/WCDMA technology. There is a diverse variety of work within Qualcomm that has the potential to allow you to move between department and get a variety of experience. Work/life balance is respected and employees are taken care of from this perspective. Pay and benefits are above the average.
Cons
Your career depends on your management and your site. Senior management appears to have good direction and run the company quite well. Based on my experience, middle management appears to be the problem. Quality work goes unnoticed, unless your project has high visibility. Many groups are quite disorganized and have little to know understanding of a proper software development lifecycle processes. There are some exceptions within the organization, but they are the exceptions, not the norm. Feedback is generally ignored at best. Promotion is based far more on longevity than on ability. This leads to a middle management that may or may not have any ability to deliver product. The company attempts to run as a large collection of independent startups with little to know oversite by the corproation. This leads to a wide variety of quality standards and no accountability for project failure.