Often we look to software to save us, or to tell us how to do our work.  This is dangerous.  The best definition as to what PM software should do for you is "to better enable processes and improve communication".

Key things improper software roll outs could lead to:
1 - software may not align with culture of how you manage projects and deliver value to your customer
2 - you become dependent on the software to run your business
3 - the software company is not agile and open to change or evolving their application
4 - ongoing licence and user costs are not properly understood and accounted for
5 - software does not integrate with other systems within the company

On the other hand, what software can do for you if properly rolled out includes:
1 - automate processes (saves time, money and resources)
2 - enables more ability to track, monitor, control and improve (data analytics and business intelligence)
3 - improve quality and reliability of what is being communicated
4 - improve collaboration outside your cubicle (geographical constraints are managed)
5 - leads to more mature business management (improves maturity level, strategy, execution, continuous improvement)

As one can see, the lists are considerable for both improper and proper roll outs.  It is critical to plan all software roll outs and ensure proper stakeholder buy in and communication has been accomplished.

Do not fall into the trap of doing nothing or waiting for the perfect software tool and the perfect price. Embrace technology but in a planned organized manner. The "train has already left the station, software is as essential to a company as telephones, pens and paper are."

If not done properly or if not taken advantage of, the consequences are critical to your business and give competitors the edge - especially now that markets are so globally interconnected and some countries are moving much more aggressively in offering better service and value due to their ability to better harness project management softwares.

Some sample links to elaborate on this subject:

Benefits & Risks of PM Software

Benefits of PM Software

Risk of PM Software