Well, one problem you might face if you get a job at a web design firm (or any other company) and try to teach English simultaneously, is that many employers force their employees to sign an agreement not to work anywhere else, similar to a non-competition clause in other kinds of contracts. Even English teaching companies themselves usually ask their employees not to work anywhere else during their term of employment. One possible rationale for this is that a competing job would presumably be a distraction from the responsibilities of the main job.
However, there are people who teach English under the table for cash or get around the rules by bartering English lessons for other benefits like meals or gifts. There are other threads on this site that discuss this dilemma in further detail; go check it out.