What constitutes a "serious" crime for the purpose of LDS baptism preparation?

Mostly its based on the discretion of the actual person getting baptized to decide what a serious crime is. If someone feels they have committed a serious crime, they will answer with yes. If someone has doubts on whether the crime they've committed is serious, the Mission President will get involved.

I believe one of the main reasons this question is asked is to find out if the baptismal candidate has ever committed murder. The First Presidency, the highest governing body in the Church, must give permission for someone to be baptized who has ever committed murder. So this question is meant to find that out so the First Presidency can be notified and can review the case in order to give or not give permission.

Another reason is to prevent sexual predators from entering the congregation unknowingly. The church will still baptize such people after having repented, but a flag will be added to their church record to prevent them from being put in a position to work with children.

And overall, the term "serious sin" is a very broad term that can possibly refer to some very horrible things, thus if someone wanting to be baptized feels they should answer yes to that question, the Church wants the Mission President to interview this person so he can make a more experienced decision and give more experienced council than a 19 year old missionary can. Its a much nicer way of accomplishing this than asking a whole bunch of question on if they've ever murdered someone, or raped anyone, or molested a child etc.

First I'd like to cite all of the clarification you quote:

Sometimes investigators may volunteer information about such sins as you teach about the commandments and invite them to make commitments. However, if they do not say anything but you think they may have a problem, prepare them for the baptismal interview by asking them if they have been involved in any of these sins. If you become aware of a serious sin, do not ask about the details of the sin. Do not schedule a baptismal date or make any promises about whether they will be cleared for baptism and confirmation. Express your love and review the principle of repentance. Kindly explain that these sins are serious and that a person with more maturity and experience (your mission president or someone he assigns) will talk with them and help them with these matters. Then send a baptismal interview request directly to the mission president.

The commandments are taught from Lesson 4 and include:

1. Pray Often
2. Study the Scriptures
3. Baptism
4. Follow the Prophet
5. 10 commandments
6. Law of Chasity
7. Word of Wisdom
8. Law of Tithing
9. Law of the Fast
10. Obey and Honor Law of the Land

Of these #3-7 and #10 are the ones I think someone could seriously break and in need of guidance from the mission president (when in doubt, it is always safer/ok to refer someone to interview with the mission president).

_{I will say that to me the first two question of interview question four are more related then the other two. If someone has commited a serious crime and a)should've gone to jail, b)was arrested for any reason but didn't go to jail, or c)did go to jail then they would be referred to the mission president.}

Misionaries are not bishops

D&C 77:104 declares that Bishops are judges. They have the keys to help people through the process of repentance. While there are specific rules concerning repentance for really bad sins (like murder), generally speaking there is no lengthy chart that explains which sins demand a bishop and which do not. We do have some general rules of conduct. Sins that involve:

• multiple people (murder, adultry, assault, all the way down to arguments that get out of control),
• that suggest the need for counseling (self-harm, habitual lying, long-term behaviors),
• that are sexual in nature,
• or that suggest apostasy (speaking or acting against the doctrines and procedures of the Church),

require a bishop to resolve. All other issues can be resolved with your personal relationship with Christ or with the optional help of the bishop. As with all things, if you're not sure, ask your bishop.

Missionaries are not bishops. They do not have the keys or authority to judge anything. They have a delegated authority allowing them to work with investigators to help them meet the basic requirements for baptism. Therefore, they can work with investigators to overcome (for example) Word of Wisdom addictions. But when it comes to issues beyond their authority that solidly block baptism (such as the bulletted issues above) someone with authority is required to step in.

In most cases, that authority is a member of the mission presidency, which has authority similar to a Stake President who, like Bishops, holds the keys to judgement. I'll leave the subtle differences between the two positions to another question.

It's worth noting that one of our Articles of Faith states,

We believe in being subject to kings, presidents, rulers, and magistrates, in obeying, honoring, and sustaining the law.

If it's illegal to own automatic weapons, then it doesn't matter how many you own. You're breaking the law of the land, and that would keep you from baptism. Again, generally speaking, if you have "paid the price" to society in terms of judgement and punishment for a crime committed against society, then you're clear. With the exception of the excpetions listed in Preach My Gospel.

As an example, when my father was serving as a Branch President, the local missionaries were teaching an ex-Navy Seal. When they got to that question, he mentioned that he had been required to kill in the line of duty. The missionaries correctly escalated this issue to their mission president, who invited my father to take care of it (the mission presidency was a long, long way away. This isn't that uncommon outside of Utah). When he interviewed the Seal, he learned that it wasn't just killing. The Seal had been involved in operations that involved sanctioned assassinations (yup, the U.S. government has a lot to answer for in the hereafter). In accordance with D&C 107:78, the issue was escalated to the office of the First Presidency and an Apostle was dispatched to interview the Seal. After lengthy discussions it was determined that all deaths were solely within the line of duty (he wasn't off the farm killing for fun, etc.), and he was cleared for baptism into the Church.

D&C 107:78) Again, verily, I say unto you, the most important business of the church, and the most difficult cases of the church, inasmuch as there is not satisfaction upon the decision of the bishop or judges, it shall be handed over and carried up unto the council of the church, before the Presidency of the High Priesthood. (Emphasis mine)

So, to really beat this horse, missionaries only have authority to assist individuals with repentance in the most minor of cases. But, no, having been a Branch President myself working closely with missionaries (and having been a missionary myself), there is no chart, sheet, book, or set of rules governing exactly when an issue must be escalated. Missionaries are expected to be obedient, honorable, inspired by the Holy Ghost, and above all, have a modicum of common sense.