One of the most difficult parts of grading is distinguishing a "first strike" or proof-like" uncirculated (i.e. business strike) coin from a proof It is important to remember that "proof 'is not a grade; it is a method of manufacture.
Proof coins are graded in a similar manner to business strike coins (i.e. Proof-1 through Proof-70). A coin which exists only as a proof, such as an 1895 Philadelphia mint Morgan dollar (if you believe, as I do, that all business strikes of that issue were melted) that is worn down to Very Good-8 grade, for example, would still merit the grade Proof-8. Of course, some proof coins are impossible to distinguish as proofs once they are worn beyond a certain point. Therefore, circulated proofs may also be graded by their circulated grade level (i.e.. VF-20 or AU-50), especially when there is some doubt as to their proof status.
When you attempt to discern between mint state and proof coins, always remember that proofs are specially made coins. They are struck under greater pressure than most business strikes, and usually they are given two or more blows of the die. In addition, they are struck on specially made, polished planchets, using polished dies (in the case of brilliant proofs.)
Therefore, consider the following factors in tandem with each other, for no single factor is enough to make a conclusive decision:
Proof Surface - A brilliant proof should have a mirror surface. In most cases there will be little if any frost (i.e. cartwheel) in the fields. There will be full mirror surfaces even in the protected areas of the field, such as between the vertical lines of the shield, in the case of Seated Liberty coinage. Matte and Roman finish proofs will also lack cartwheel, and will have either dull or satiny surfaces.
Of course many business strikes have mirror or prooflike surfaces. Both prooflike business strikes and proofs will usually have some hairlines. However, business strikes are far more likely to have bagmarks as well as hairlines.
Strike - Proofs tend to be somewhat sharper than business strikes. In
fact, most proofs are fully struck. There are a number of
exceptions however. The most common exceptions in the
Morgan dollar series are the proof issues of 1891, 1892 and
especially 1893. These dates are often found weakly struck in the
Edges - Most proofs will have either square edges, or wire edges in the
case of some matte and Roman finish proofs. Business strikes
usually do not have square or wire edges.
Die Variety - Proofs were usually struck from one or two pairs of dies, and these dies were often used solely for proofs. Therefore, any coin struck from proof dies is at least somewhat more likely to be a proof. Die variety, while not conclusive, can be an important factor in determining proof status.
Lint Marks - Proof dies and planchets were usually polished with soft cloths. Occasionally, pieces of lint would adhere to the die or planchet prior to the striking process. Therefore, lint marks are fairly common on proof coins, yet rare on business strikes.
Lint marks are discernible from scratches because they are more even and uniform in intensity. They tend to be more curved than scratches. Furthermore, unlike scratches, they aren't surrounded by displaced metal.
If you aren't sure if a coin is proof, and it has one or more lint marks, the chances are good that it is a proof.
Learn how to weigh these factors together. Combined with your own experience from looking at coins, you should be able to tell most proofs from most business strikes. Like grading, the attribution, "proof," is at least partially subjective. Experts often disagree about whether a coin was struck as a proof. If you have any doubt, it is best not to buy the coin unless you know your dealer and he is willing to guarantee, in writing, that the coin you are purchasing is indeed a proof. Otherwise, reconsider whether or not you would wish to own a coin which experts may never unanimously attribute as a proof.