If you're going to build an earth oven, you can expect some cracks.
Generally, but not always, cracks do not have an impact on the integrity of the oven. Nobody, however, really likes to look at a cracked oven, but after you insulate and then apply stucco, the cracks may be hidden from view.
Consider making a mini-oven (photos on this blog) before you make the "real thing." Spend some time experimenting with your clay to sand ratio, remembering that too much water in the mix will make the walls slump. Not enough water in the mix will prevent the clay and sand from fusing, and your oven can fall apart. Too much clay is really asking for severe cracking, but not enough clay could cause your oven to fall apart.Too much sand, and your oven can also fall apart. It's not so simple, regardless of what anyone tells you.
Try two parts sand to one part clay, using just enough water to make it all cohesive.I like to cut the opening right after the dome is complete, lighting a small fire to dry it out slowly.
You could patch the cracks with clay slip or temporarily with bread dough.
You might prefer, however, to drape a metal roof over the oven and simply forget about it.