Ellos lo hacen de manera que no (haber) errores.
Why is this haya and not hay? The main clause is in the indicative.
When exist a possibility you use the subjuntivo.
When it is true or if you have the possibility implicit, you do not use the subjuntivo.
ellos lo hacen de manera que no haya errores, tienen un buen departamento de control de calidad.
ellos lo hiceron de manera que no haya errores, vamos a probarlo.
ello lo hicieron de manera que no hay errores, estoy sano y salvo.
The last can be said in a better way, but works.
First of all, I'm not an expert in grammar.
But my idea is that subjuntive in clauses introduced by que are used when the second verb denotes an action related to the subject of the first one, but the first person is not the actual subject. The usual cases are when the first verb denotes emotion, but also responsibility, intention or similar things:
Me alegro de que no haya errores.
Intenta que no haya errores.
Ellos lo hacen de manera que no haya errores.
But:
He visto que no hay errores.
The subjuntive will also be used when the first verb is impersonal:
Es importante que no haya errores.
No importa que no haya errores.
It is worth noting that similar phrases using si instead of que will not usually have the subjuntive:
No importa si no hay errores.
Me enfadaré si hay errores.
Subjunctive here would be the most common choice, because it's they are doing things such that, or with the intended goal of (there is no way to know that will be the actual result of their action). Compare to "lo hicieron para que no hubiese errores".
However, as Helmut points out, when what comes in the subordinate clause is not the goal, but rather the result, then indicative is the correct choice. Compare to "lo hicieron de una manera paricular, así que no hay errores".
The "idiomatic" English translation is, "They do it this way so there won't be errors."
But a more accurate translation is, "They do it this way so there should not be errors" (subjunctive). The Spanish form, haya conveys this sense, the English does not.