The main hazard from re-use of wood is damage to tools from nails, screws etc. embedded in the wood. Even a small panel pin can ruin a plane iron or wood chisel.
It is also possible but less likely for such items to be thrown out by power tools and so be a hazard to the wombler.
Old wood often has a lot of splinters and these can be a hazard to un gloved hands. Pallets are particularly prone to this. Pallets are also prone to having very hard knots and other defects in their planks.
Look carefully at any holes in your recovered timber, especially around joints or where hinges etc. were attached to ensure that there are no nails or broken screws below the surface. Old floor joists are particularly prone to this sort of contamination and floorboard nails are very substantial obstacles to saw blades. Pallets are usually held together by barbed nails that often break off when extraction is attempted.
Other hazards are dust from MDF, chipboard and lead based paint (when sanded off) which can be harmful if ingested.
Watch out with wood from pallets. Pallets used for international shipment have to be treated to reduce the risk of shipping insects between countries. Most nowadays are heat treated and are fine to use, but there are still a fair few about that have been fumigated or soaked in really nasty insecticides. Turning this into sawdust is really quite unhealthy. Look for an "HT" mark (Heat Treat) and GET RID of any pallets marked "MB" (Methyl Bromide).