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Rooting or jail-breaking your device could disable built in security features of your phone, like the firewall, and could install malware on your computer.
This can make it difficult to regularly pull down security updates and other patches for the device.
Ensure that your device is configured to automatically install updates as they become available.
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Resources
Traveling Overseas with Mobile Phones, Laptops, PDAs, and Other Electronic Devices - The National Counterintelligence and Security Center
Prepare Your Laptop for Traveling - Brown University
Travel Safety and Securing Technology - Indiana University
Securing Mobile Devices When Traveling - Indiana University
The Traveler's Guide to Cybersecurity - Syracuse University
Recommendations for Travelers to High Risk Countries - Stanford University
Safety and Security for the Business Professional Traveling Abroad - Federal Bureau of Investigation
Source: Effective Practice: Cybersecurity for the International Traveler from the Research and Education Networks Information Sharing and Analysis Center (REN-ISAC)