Everything Under the Moon

Luckily this has only happened to me a few times, and only partially, but what do you do when you are in the middle of a ritual and you are interrupted by something "mundane" that absolutely requires your attention? Say, for instance there is a knock on the door, or a family member has a pressing need (or maybe if they don't understand your magical practice, a not-so-pressing need). Or here's one that concerns me, although it has thankfully never occurred so far: what if you're mid-ritual and you see a spider in the room? (It might sound like a joke, but as a severe arachnophobe, there's no way I could concentrate properly on a ritual if I saw a spider).

What do you do?

Well, this has happened to me before. And no, the spider thing doesn't sound silly, not to me - I am the same way.
To answer your question, I started the ritual from the beginning when I got interrupted. But this kinda depends on your beliefs. Being interrupted during ritual may mean you are not to perform it at all.
I would do some divination work to find out what to do next.

I keep getting interrupted *grrr* once I started new. Two times... then I just picked up where I was.

Since it wasn't much of a spell. Just cleansing that one particular time.

Yex, I understand about the spider. When I was dedicated to this path my fear of spiders was huge. Once I began to learn the mythologies of various cultures, Native American in particular, and the idea behind the weaver, I began to lighten up on my attitude about spiders. Still don't want one on me, but I'll entrap them in a drinking glass, slide a stiff piece of mail under the glass between the wall/floor, and take em outside. I can now marvel at the beauty they create.
But back to the main issue.
Interruptions can really ruin a ritual and it can be difficult to regroup. There are a few steps you can take...a do not disturb sign on the door...notify others in the house your need for some time alone and undisturbed...phone off the hook or turned off...children however may take precedence, depending on their issue. As long as they aren't bleeding or puking or some other dire issue that needs immediate attention, help them to understand that this is your time with spirit. They may want to join you, but attention spans can be short. As long as you can instill in them that is a sacred time and to be respectful, they may quietly slip in and out of circle. In my group we have had many children and have accepted the fact that they come and go during circle. If they get unruly it is up to the parent to remove themselves and the child from circle.
There are other unforseen situations that may cause you to fold it up for the time being, a story that comes to mind was when the Sheriff's and the Fire department drove back to where our circle was meeting, because they were sure we had a fire (in an area where fire is not allowed) that really squelched the energy, we packed up and went home. We have had drama within the circle too that gets disruptive, couples fighting, members claiming the God is riding them or other possessions, visions that are too horrible to comprehend, people passing out or being otherwise overwhelmed, nervous newcomers squeezing and crunching thier water bottle or reciting hail Marys or crossing themselves, accidental fire divers or Altar divers. The list goes on...if the circle le isn't totally breached you may be able to regroup by taking several cleansing breaths, re visualize the circle, chant for awhile or Om ....asking the Gods and Goddesses if they feel it is ok to proceed, most times you can move forward.
Then there is planetary influences, try to do your work during favorable aspects and you will likely have less trouble. Void of course Moon is one that can make for wonky circle, but then I have worked wonderful circles during that time.
Blessings, Firebird

When I get interrupted and my concentration is broken, I feel disoriented, edgy, and startled. Grounding myself, and all energies and intentions that were raised fixes the immediate problem. Then I have to decide if I want to regroup and restart from the beginning or if it's OK to even continue.

Some things may seem like interruptions but are Nature joining in the fun. The curious come to watch. Some deep breaths help steady the nerves and you can acknowledge them. Maybe even ask/insist that they leave. That's one use for the broom.

I don't understand the spider phobia. I don't understand snake phobias either. When I have been interrupted, I "put things on hold," then take up where I left off.

Snow

I've been interrupted twice. It really grinds my ancient gears when this happens.
Any ideas on how to deal with annoying neighbors that like to peek in?

Ignore them if possible. What they think has no bearing on your craft. However, if it is a distraction try curtains or something that blocks or hinders direct line of sight. Sometimes the most basic solution is the best I have a friend who has some thin material black curtains. That block sight but still allow some light through. I'm not sure what they are made out of but I want some.