There are lots of things in the work of the parish priest that still throw me. One of them is non-Catholics who come to confession. This happens more often than you might think. It seems to me that there are three fairly distinct types, which I present in ascending order of difficulty:
There are the catechumens or (more likely) pre-catechumens, who have a desire to seek God's mercy and forgiveness, or at least experience sacramental absolution. Either they just can't wait, or are confused or uncatechized about how the sacramental economy works. These aren't too hard to deal with, because they desire the sacraments at some level--and sometimes very intensely. I pray with them, give them some spiritual counsel, and try to explain to them that they should desire baptism all the more because of the forgiveness of sins it will bring. Then, if they should--God forbid--sin after their baptism, confession is there for them.
Then there are souls who seek God's forgiveness, or at least the therapeutic act of confession on the natural level, but who just aren't Catholics or a member of any of the apostolic churches that retain the sacrament of penance. It's easy to tell them apart from the Catholics; confession is a private and individual thing, but it's also a fairly scripted encounter. There are many versions of the script, but chances are that you tend to begin your confessions with one formula or another, have a favorite version of the Act of Contrition, etc. When someone comes in with no script or even 'confesses' not knowing how to 'do it,' I know it's time to see if the 'penitent' is even a Catholic (It is necessary to check, as he might be a baptized but totally uncatechized Catholic.)
If the person is an adult I usually ask him directly if he is a Catholic. If not, I try to find out if he is at least validly baptized, which people rarely seem to know. With kids the question is more delicate. My experience with Catholic children and teenagers is that they often don't know how to go to confession (I think that some religious education programs teach it in such a way that 'first reconciliation' is a nice celebration, but doesn't leave behind a portable skill), so if I suspect that a young person is not a Catholic, I ask them if they have received the sacrament of Confirmation. If the answer comes back, "Huh?," or "What's that?" I'm pretty sure that I have a non-Catholic. Having found out what I can, I let the 'penitent' confess as she or he needs to, explain to them why we are either not celebrating a sacrament or doing so in a very occult way, pray with them in thanksgiving for God's mercy, and send them on their way.
The final category is the hardest. These are the non-Catholics who are sent into confession by someone else. It might be a devout, well-meaning, but ultimately controlling and misguided spouse or significant other who thinks the person needs confession, penance, and absolution. Many times it is an aunt, uncle, or grandparent sending in non-Catholic child or teenager in an effort to make up for a lack of or incorrect (in their estimation) religious upbringing. In these cases I hear whatever 'confession' someone wants to make, but I also explain to them that this not a good use of the "sacrament," that they really should neither be there nor let anyone send them back. If it's a child, I tell them to send anyone who tries to make them "go to confession" to me, and I promise to deal with them.
All of these procedures are subject to abbreviation and/or the request to move the conversation to another time and setting if the line for confession is long or if I have to get to something else right after the end of scheduled confession time. Baptized Catholic Christians have a right to the sacraments that other baptized or unbaptized people do not enjoy in the same way.