Paraphrasing the Summa: First part, Question 3, article 6

Article 6. Whether in God there are any accidents?

*Accidents - He's not talking about mistakes.  Although, in God, there are no mistakes either.  St. Thomas is referring to nonessential properties.  Accidents are nonessentials.  Such as, it is not not essential for the definition of human that they be American.    Therefore, American is a nonessential property of some humans.

Since we are Catholic, we believe that having a rational soul is essential to being a human.  I believe, that is possibly the only essential that is recognized for a human.  

So, we could paraphrase this to say:

Whether all God's properties are essential to His Being God? 

Objection 1. It seems that there are accidents in God. For substance can not be an accident, as Aristotle says (Phys. i). Therefore that which is an accident in one, cannot, in another, be a substance. Thus it is proved that heat cannot be the substantial form of fire, because it is an accident in other things. But wisdom, virtue, and the like, which are accidents in us, are attributes of God. Therefore in God there are accidents.

The first objection says that God's properties are nonessential because they are shared by many.  Thus, God is wise.  But so are some men.  Therefore, we can't say that God is God because He is wise.

Objection 2. Further, in every genus there is a first principle. But there are many "genera" of accidents. If, therefore, the primal members of these genera are not in God, there will be many primal beings other than God--which is absurd.

The second objection says that nonessential properties abound and   are shared by many creatures.  But all creatures can be traced to a first of its kind.  If there are many Firsts, then there are many Gods.  And this is not true.
*That objection, sort of disproves itself, in my opinion.

On the contrary, Every accident is in a subject. But God cannot be a subject, for "no simple form can be a subject", as Boethius says (De Trin.). Therefore in God there cannot be any accident.

To understand this, we must define the word, "subject".  Subject means many things but the meaning in context of this statement is, "material or substance".

From Merriam Webster's online dictionary:

Full Definition of SUBJECT

1

:  one that is placed under authority or control: as 

a  :  vassal

b (1)  :  one subject to a monarch and governed by the monarch's law (2)  :  one who lives in the territory of, enjoys the protection of, and owes allegiance to a sovereign power or state 

2

a  :  that of which a quality, attribute, or relation may be affirmed or in which it may inhere 

b  :  substratum; especially  :  material or essential substance....

We know, from Question 3, Article 2, that God is not a material  nor a substance.  So, St. Thomas counters with the fact that only materials or substances have nonessential properties.  Therefore, God can not have those.

I answer that, From all we have said, it is clear there can be no accident in God.

Therefore, God can not have nonessential properties.

First, because a subject is compared to its accidents as potentiality to actuality; for a subject is in some sense made actual by its accidents. But there can be no potentiality in God, as was shown (2, 3).

First, substances are, in a manner of speaking, defined by their nonessential properties.  Thus, a human being has 10 fingers and toes. But so do most apes.

But God does not have nonessential properties by which He might be defined.  God is Divine.  Only God is Divine.  God is immortal.  Only God is immortal.  God is all knowing.  Only God is all knowing.  These are all ESSENTIAL properties of God. 

Secondly, because God is His own existence; and as Boethius says (Hebdom.), although every essence may have something superadded to it, this cannot apply to absolute being: thus a heated substance can have something extraneous to heat added to it, as whiteness, nevertheless absolute heat can have nothing else than heat.

God is absolute.  Nothing can be added to Him because He needs nothing and possesses everything.

Thirdly, because what is essential is prior to what is accidental. Whence as God is absolute primal being, there can be in Him nothing accidental. Neither can He have any essential accidents (as the capability of laughing is an essential accident of man), because such accidents are caused by the constituent principles of the subject. Now there can be nothing caused in God, since He is the first cause. Hence it follows that there is no accident in God.

God is essential to all creation.  Therefore, He is the First Cause of all things in creation.  Therefore, those things which are nonessentials in creatures are caused by God's essential nature.  Nothing can be caused in God, but God is the cause of all things.

Reply to Objection 1. Virtue and wisdom are not predicated of God and of us univocally. Hence it does not follow that there are accidents in God as there are in us.

The properties which we share in common with God are nonessentials in us.  But they are essentials in God.

Reply to Objection 2. Since substance is prior to its accidents, the principles of accidents are reducible to the principles of the substance as to that which is prior; although God is not first as if contained in the genus of substance; yet He is first in respect to all being, outside of every genus.

I don't think he means, "prior in time".  I think he means, "in order of importance".  Thus, men (substance) have ten fingers and toes (accidents).   But, if a man does not have ten fingers and toes, he is not declassified to another species or substance.  

But God is not a substance.  So, He has no accidents and this objection does not apply to God.