Are things commonly blessed by priests at certain times of the year appropriate to bring to a priest for a special blessing? Is it appropriate to ask priests to bless things like oil, salt and water that you bring to them for a blessing? I was reading this answer and was wondering if it made sense for a layperson to bring things like salt and oil for a blessing.  Would a priest be responsible for making sure that the thing they're blessing really is salt, oil and water?
Are things commonly blessed by priests at certain times of the year appropriate to bring to a priest for a special blessing?

The short answer is yes. 

But before doing so make arrangements with your pastor or priest before doing so.

This is something I do, not on a regular basis, but now and again.

As far as I am aware table salt and saltpetre are considered salt and both are edible; thus either one may be used in the blessing of salt. Normally, only table salt is employed.

Some blessings in the Roman Ritual are reserved to one particular feast in the year. Therefore, please make arrangements with your pastor or priest beforehand. Over the years I have had the occasion of getting many diverse these objects specially blessed by the Church with the help of her sacred ministers.

According to the ancient Rituale Romanum several blessing are reserved to specific feasts and/or bishops or even the pope such as the following: 


Blessing of Water (Magi Water) on Eve of the Feast of the Epiphany (January 5). In the Extraordinary Form, the permission of the local ordinary (bishop) is required for this blessing because it contains a major exorcism prayer within it.
Blessing of Gold, Frankincense and Myrrh on the Feast Epiphany
Blessing of Chalk on the Feast of the Epiphany
Blessing of (Domesticated/Farm) Animals on the Eve of the Feast of St. Anthony of the Desert (January 16)
Blessing of Throats on the Feast of St. Blaise
Blessing of Herbs on the Feast of the Assumption
Blessing of Seeds on the Feast of the Nativity of the Most Holy Virgin Mary
Blessing of Basil on the feast of the Exaltation of the Holy Cross
Blessing of animals (pets) on the Feast of St. Francis of Assisi (October 4)
Blessing of Hunting Hounds on the Feast of St. Hubert (November 3)
Blessing of Water, Salt and Bread on the Feast of St. Hubert (Page 466) See: Buns for Saint Hubert
Blessing of the Sword and Hat on Christmas Eve  (December 24) This blessing is reserved to the pope and has not been done in modern times.
Blessing of wine on the Feast of St John the Apostle (December 27)


This is not an exhaustive list. Some dioceses and Religious Orders have the privilege or  reserved right of blessing certain religious items or sacramentals. 

Some of these blessings are simple blessings. A few are known as containing a minor exorcism. One is actually a major exorcism and the bishop’s permission is required to confer the required blessing.  


  According to Catholic belief demons or fallen angels retain their natural power, as intelligent beings, of acting on the material universe, and using material objects and directing material forces for their own wicked ends; and this power, which is in itself limited, and is subject, of course, to the control of Divine providence, is believed to have been allowed a wider scope for its activity in the consequence of the sin of mankind. Hence places and things as well as persons are naturally liable to diabolical infestation, within limits permitted by God, and exorcism in regard to them is nothing more that a prayer to God, in the name of His Church, to restrain this diabolical power supernaturally, and a profession of faith in His willingness to do so on behalf of His servants on earth.
  
  The chief things formally exorcised in blessing are water, salt, oil, and these in turn are used in personal exorcisms, and in blessing or consecrating places (e.g. churches) and objects (e.g. altars, sacred vessels, church bells) connected with public worship, or intended for private devotion. Holy water, the sacramental with which the ordinary faithful are most familiar, is a mixture of exorcised water and exorcised salt; and in the prayer of blessing, God is besought to endow these material elements with a supernatural power of protecting those who use them with faith against all the attacks of the devil. This kind of indirect exorcism by means of exorcised objects is an extension of the original idea; but it introduces no new principle, and it has been used in the Church from the earliest ages.  - Exorcism (Catholic Encyclopaedia)


I get a priest to bless olive oil during Eastertide when possible. Like I said above, I ask the pastor a week or two before so he is not taken by surprise. Unlike most of the faithful I bring along holy water (aqua benedicta) and a copy of the prayer I desire the priest to employ.