People with stronger foreign accents could be seen as less trustworthy than people with native ones. Researchers from the University of Chicago asked participants to judge the truthfulness of statements by native and non-native speakers. To try and get around the problems of prejudice the participants were told that those reading the statements were simply reading out material prepared by other people. The participants gave the native speakers an average score of 7.5 on a 'truthfulness' scale compared to 6.95 for people with mild accents and 6.84 for people with heavy accents. In a second experiment participants were also told the purpose of the experiment. In this study the people with mild accents were rated as being as truthful as those with native accents but the people with stronger accents were still rated as being less truthful.
You can find out more about this study by clicking on the link within the title of this post.