How can a global project be more complex than a project performed within just one country? How might these elements affect the successful outcome of the global project?

A global project by definition is a project that is implemented in multiple countries. The project could be piloted in one country and replicated anywhere else. For example a global technology project in the US that is introducing businesses to the use of technology for transmitting market related results can face numerous challenges in other countries.
These challenges could include collecting and accessing the results in a timely manner, time differences, policy limitations that could require adequate time for approval of results, and difference in labor skill set.
To address these issues and make the project successful globally, the project designers would need to understand all the laws in all the different countries pertaining to technology; identify and partner with the key players in the different countries; establish the right parameters for implementing the project which would be the minimum requirements to succeed; have a flexible strategic plan that is reviewed frequently to determine the success or failure of the project, and quickly revise the strategy to correct any problems.
It would also be critical to create a working model in countries that have similar business environments.  This model can then be customized for a set of countries, lessons learned and transferred to the next set of countries, until success is achieved in every targeted country.
The project manager would need a global outlook to ensure successful replication of the project globally.  The project manager would understand clearly that the conditions vary from country to country and that success in one country might not necessarily translate to success in another country.  Understanding the global market conditions will be critical to achieve success.
 

In addition to having far more moving parts, a global project is far more complex than one within one nation because one must take into account the differences from one country to another. Let us consider a few of these.
First, if one is operating in more than one country, one must take into account cultural differences. These include language, dress, religion, and customs. Without having someone on the ground who speaks the language, it is difficult to operate. Even when someone does speak the language, there are bound to be local idioms that must be learned. In many Muslim countries, sending a woman with an uncovered head and bare arms to head a setup operation is, to put it mildly, a blunder. Scheduling an important meeting on a Saturday in Israel, the Jewish day of worship, is not going to win friends and influence people. In many countries with a hot climate, there is no work during the worst heat of the day. Trying to get a workforce to disregard this custom is a recipe for disaster. A global operation must account for a myriad of countries and cultures. 
Second, there is a political and legal environment that must be considered. To be successful, you cannot run afoul of the laws of the countries in which you want to operate. Sometimes, a political hierarchy must be considered, so that one approaches the powers that be in a given country in the proper order. In some countries, bribery is the norm, which makes it difficult for American companies to compete, as they are not permitted under American law to bribe in foreign lands. Whatever the laws are of the country in question, they must be obeyed, which makes global projects quite complex.  
Third, there are geographical considerations that make any project more complex. When a CEO is sitting in the office looking at a map, deciding to open five more factories in five different countries, he or she must consider the terrain, weather, flora and fauna, and, one hopes, the environmental impact. Is the company building on bedrock or sand? Could monsoons sweep a building away? Ebola or dengue fever might be rampant in the area. That surely should be something to consider. The site might need to be cleared of trees that should be preserved. Each country and each new site will create unique challenges for the project.
The global economy represents new and exciting opportunities for business, but it is vital to remember each country is different. The cultures, political and legal environments, and geographical features will always vary. Inevitably, this makes any project more complex than a project done solely in one's own country.