Ambient service temperatures
Although a standard 308 type filler can be used for joining a 304 type stainless steel to carbon steel, more highly alloyed fillers, such as the 309 type (23 12L to EN 12072) are preferable. This is should help avoid cracking in the weld dilution zone that can be a problem if a 308 type (19 9L to EN 12072) filler is used, where there can be too low a ferrite level and martensite may also be formed on cooling.

Elevated temperature services temperatures (over 425C)
If the welded parts are for higher temperature service, then the differences in thermal expansion rates of the steels and filler can lead to thermal fatigue cracking. Long exposure times at these temperature of welds with enhanced ferrite levels can result in embrittlement due to sigma phase formation. Nickel based fillers (Inconel) produce welds with lower thermal expansion rates than the stainless steel fillers and so may be preferable.

Risk of bimetallic corrosion at welds between carbon and stainless steel
Unprotected welds subject to aggressive environments such as immersion in seawater could result in sacrificial corrosion to the less noble carbon steel part. However, post weld surface coating repair would normally be needed to the carbon steel to 'restore' the corrosion protection.

If this re-coating / painting is allowed to lap over onto the weld bead then the joint should not be at risk to bimetallic corrosion in any environment so long as the coating is sound. Ideally the weld bead should be covered so that only the 'parent' stainless steel is ultimately exposed. This ensures that galvanic corrosion cells cannot be set up across the joint, where there is a composition 'gradient'.