Can I use actual mirrors in a solar oven build or will I set something on fire?

I would like to use actual mirrors inside the box and as reflectors around it - is there any issue with that? It gets really dry here in the summer. Would I accidentally set something on fire?

I would be concerned about the mirrors breaking from the heat.  Telescopes use mirrors, but those are first service mirrors ( the reflective material is on the outer surface).  Household mirrors have the light pass through the glass to the reflective surface then it passes back through the glass again.  I doubt if the glass is manufactured to withstand the heat.

The mirrors won't get hot. Aiming the mirrors at a designated focal point and keeping flammables out of that hot zone should make a safe oven.

Even low melting glass doesn't melt until about 500C/950F [1] so the absolute temperature of the glass should not be an issue unless your oven is starting to resemble a kiln. While glass has a high melting temperature, some of them don't handle rapid or uneven heating very well. If you are focusing a lot of energy into one small area of the mirror, that could cause it to crack due to the heated part expanding while the unheated part stays the same size.