What are the differences in design considerations for ground attack and air dominance aircraft?
One thing to note is that 'pure' air dominance fighter or ground attack aircraft is not being developed anymore. Most of the combat aircraft developed recently/under development are multirole (or 'omnirole') aircraft.

In case of air dominance (or air superiority) fighters, which have the task of eliminating enemy air defense system especially fighters and securing aerial control for operation of friendly forces without harassment, the following are important design objectives:


High thrust to weight ratio, as it helps in maneuvers.
Stealth, as the enemy can't shoot what he/she can't see.
High maneuverability, for close combat situations and evasion. 
High weapons load, as it enables engagement of a large number of enemy aircraft at once.
A good range, as it is better to engage enemy aircraft in their area rather than in friendly territory.
A powerful radar to track and engage enemy aircraft, as it enables them to shoot first.
Communication links to transfer data between the aircraft and between the AEWACS aircraft, as most of the aircraft today operate in an integrated battlefield.
Speed is also a very important parameter.


In case of ground support (or attack) aircraft, whose primary task is the destruction of enemy logistics and/or support for ground troops under fire, the designers look for similar yet a bit different set of characteristics. 


Ruggedness, as the aircraft should be able take some amount of punishment and return home.
High endurance and Time on Target, as the ground troops may require support for an extended period of time, with corresponding weapons load.
Communication links between aircraft and ground troops for obvious reasons.
Precision targeting systems for situations where friendlies are in close contact with the enemy troops.
Ability to operate from forward operating bases is desirable.


Most of the present generation aircraft carry out their ground support duties using precision weaponry rather than any fundamental design decisions. Though there are still trade-offs, as in any aircraft design.


The weapon load of stealth aircraft is lesser their non-stealthy counterparts as external weapons carriage increases the radar signature of the aircraft.
For ground attack aircraft, a high subsonic speed is more than enough unlike the supersonic air dominance fighters.
Low altitude maneuverability is important for ground attack aircraft for quick ingress and egress from the combat area. 


One aspect of aircraft design is that combat aircraft optimized for high altitude operations can face higher stresses when operating in lower altitudes (i.e. near ground). For example, when USAF switched B-52s from high altitude bombing role to low altitude penetration tactics, it caused increased stress in the airframe.