To expand on Joonas's answer, I think he is 100% correct that mirata is elliptical; est is left out but must be assumed in order to translate the sentence. The structure is as follows:
Iuno despexit in Argos
et mirata [est] nebulas volucres fecisse faciem noctis
nec sensit [nebulas] remitti tellure
We have three parallel main clauses here, separated by the coördinating conjunctions et and nec. Within the second clause, there is an accusative with infinitive that depends on / is governed by the verb mirata; the third clause* also contains an a.c.i., depending on sensit.
In your quotation, est must have been left out. The coördinating conjunction et forces us to read it as something that is parallel with what came before it; because it cannot be parallel with a single noun or a noun group, or whatever, that came before et, it must be parallel with the entire clause before it (Iuno aspexit...), which means that it must itself also be a full clause with a finite verb (mirata est...).
An English aequivalent would be thus:
Juno looked down and amazed that ...
It seems clear that was must be supplied, or the two parts cannot be properly read together.
If there had been no et, then the opposite would have obtained:
*Iuno despexit in Argos
*mirata nebulas volucres fecisse faciem noctis
The English aequivalent would be thus:
Juno looked down, amazed that ...
The participle would have had to be dependent on the previous clause, and one (full) clause can only depend on another clause (= be subordinate to it) if it is introduced with a subordinating conjunction or a relative pronoun, which is absent here. It follows that mirata could not have been a full clause, and the whole phrase would have been just a participial phrase (a participle with some arguments), just as in the English example.
As to whether participles can govern infinitives and indirect speech, the answer is yes. A participle is both an adjective and a verb at the same time. Externally, it is an adjective, since it must normally agree with a noun or pronoun (although those can be implicit—but that is also the case with adjectives). That's why participles have the same endings as adjectives.
laudo canem mordentem = I praise the biting dog
curo canem vulneratum = I care for the wounded dog
Internally, however, it is a verb, which means that it can often have the same arguments that any other verb can—arguments that depend on it / are governed by it.
laudo canem mordentem inimicos = I praise a dog biting enemies / that bites enemies (a direct object normally occurs only with verbs)
curo canem vulneratum ab inimico = I care for a dog wounded by an enemy / that is wounded by an enemy (ab "by" normally occurs only with verbs)
So mirata can govern an a.c.i. just like any other verb.
*) By "clause" I always mean a full clause, i.e. a finite verb with its dependencies—the conventional meaning of the word clause as something closed off and complete.
