Tim O'Shea, vice president of consulting services at Graebel Relocation, told SHRM that mobility managers in recent years have eliminated certain costly benefits, such as trips abroad to look for housing.  

"We know this can meet the needs in the short term, but wonder how lower-cost alternatives will impact overall employee experience and productivity. That remains to be seen," he said. 

The next biggest concern for mobility managers — cited by 62 percent — is compliance with laws and regulations relating to relocation of employees abroad. 

Amidst heightened awareness of international terrorism, immigration law becomes an even bigger headache for employers trying to move workers around the world — 63 percent of mobility managers reported experiencing longer waits for visas this year than last. 

"It is a good idea [for relocation managers] to meet with human resources and business leaders on a quarterly basis to set proper expectations for visa timing and complexity," Matt Spinolo, executive vice president of global client services at Cartus, told SHRM.

The number three concern, cited by 44 percent, is compensation, allowances and payroll. It's a concern every HR manager is familiar with, but when dealing with employees in different countries, those familiar concerns can be further complicated by exchange rates and currency fluctuations. Just over half reported having trouble dealing with changes in the value of another currency. 

Another very common concern, even if it's not the biggest one, is finding spots for employees' children in international schools. Seventy-seven percent of those surveyed reported a lack of space in desired schools as a challenge for them and their workers.