Sometimes the greatest risk of going to Cartagena is not wanting to leave as said in this great Colombian advertisement: El riesgo es que te quieras quedar https://www.youtube.com/watch?v=8kUU-DWOqmI

There are several work possibilities for foreigners who want to stay in Cartagena (though, be prepared for some stiff competition!)

Language Centers (English, French, German …):
El Centro Colombo Americano, Cartagena: www.colombocartagena.com
Alianza Canadiense de Idiomas: www.aci.edu.co
Academia de Idiomas Smart: www.smart.edu.co
Alianza de Colombo Francesa de Cartagena: alianzafrancesa.org.co
Bi-lingual, prívate schools (for certified teachers with international experience):

Colegio Montessori
Colegio Britanico
Colegio Jorge Washington
Liceo Frances

Volunteering:
Cartagena’s Colonial beauty and enchanted balconies are a backdrop to one of Colombia’s most impoverished cities. NGOs abound and are always looking for professionals and volunteers to help. Here’s a solid list of organizations in Cartagena that work with an array of vulnerable populations, nature conservancy and more. Do your homework to make sure they’re what you’re looking for.

http://www.charity-charities.org/Colombia-charities/Cartagena.html