Mientras + Subjuntivo/Indicativo
"Mientras" is one of the subordinating conjunctions introducing time clauses in Spanish, and as such is followed by Subjuntivo when we're talking about a still unaccomplished action, one that will be done in the future and by Indicativo when the action is already done in the past or is being done now, in the present.
Having this in mind, in the following sentence, I used Subjuntivo:
Lava los platos, mientras yo (poner) ponga la mesa.
Here we have an Imperative form of the verb "lavar", which indicates that the action is still unaccomplished...
That's why I put the verb in Subjuntivo, but I'm not fully sure, so can someone say if I'm right or no (and if "no", then, of course, why)?
With "mientras" it's important to know whether or not we're talking about a simpe coexistence in time (indicative) or if there's a condition or cause-and-effect involved (subjunctive).
In your example above, the focus is that the two things can be done simultaneously; one is not really dependent on the other, so indicative is appropriate.
Borrego et al, "El subjuntivo: valores y usos" gives this interesting example:
a. No atacarán mientras estamos despiertos (simultaneidad: 'No atacarán durante el tiempo que permanezcamos sin dormir').
b. No atacarán mientras estemos despiertos (condición: 'No atacarán si no nos quedamos dormidos').
Hope this helps
No, it should be in indicative form. Although the washing of the plates is incomplete, it is taking place in the current tense so it should not trigger subjunctive.
As you said in your (awesome) explanation of subjunctive use with "mientras," subjunctive should not be used when the action is in the past or present.
A command is technically in the present tense, so this would not use subjunctive.
Another interesting case in which the subjunctive is used with "mientras" is when the speaker is making a proportionate comparison about the future or a hypothetical situation. Por ejemplo: "Mientras más cervezas bebas, más querrás beber" which translates: "The more beers you drink, the more you will want to drink". As far as I know, In Spain the more common construction would be to use "cuanto" instead of "mientras", giving you: "Cuantas más cervezas...."