This appears to be the relevant part:

In very exceptional circumstances, where it can be demonstrated that an obvious refereeing error has occurred, a player or his club may submit a Claim of Wrongful Dismissal in respect of the following offences of:

Has an obvious refereeing error occurred?

http://tinyurl.com/yzstv6p

3.2 Players Sent Off for Serious Foul Play, Violent Conduct or Spitting at an Opponent or Any Other Person
A player who is sent off for serious foul play, violent conduct or spitting at an opponent or any other person, will have 12 penalty points added to his applicable League disciplinary record. In addition, he will automatically be suspended in accordance with the provisions of Paragraph 3.8.

3.8 Serving of Suspensions
Suspensions incurred by players shall be served in the competition in which they are incurred and shall be measured by the relevant team of the club (i.e. the team in which the player normally plays) playing the requisite number of matches.
The following qualification applies:-
– A player who is sent off for serious foul play or violent conduct is suspended automatically until such time as his club’s team(s) has completed a match in a competition for which he would otherwise be eligible for selection.
– A player who is sent off for spitting at an opponent or any other person is suspended automatically until such time as his club’s team(s) has completed its next two matches in competitions for which he would otherwise be eligible for selection.
(Please refer to Appendix 4 – Guidance Notes on Serving of Suspensions).

http://tinyurl.com/yzql5r8 – Review Panel

1. The Review Panel (“Panel”) is a sub-committee of the Disciplinary Committee which has responsibility for:
i) considering and investigating Claims of Mistaken Identity
ii) considering and investigating Claims of Wrongful Dismissal
iii) determining whether or not there is a case to answer in regard to a player’s act of misconduct which has been brought to the attention of the Disciplinary Committee/Review Panel by means other than a match official’s report.
If it is decided that there is no case to answer, no further action will be taken against the player.
If it is decided that there is a case to answer, the matter will be referred to the Disciplinary Committee for investigation and/or consideration.

http://tinyurl.com/ya2god8

2. CLAIMS OF WRONGFUL DISMISSAL
In very exceptional circumstances, where it can be demonstrated that an obvious refereeing error has occurred, a player or his club may submit a Claim of Wrongful Dismissal in respect of the following offences of:
? Serious foul play
? Violent conduct
? Spitting at an opponent or any other person
? Denying the opposing team or an opponent a goal or obvious goalscoring opportunity as defined by Law 12
For the avoidance of doubt, Claims of Wrongful Dismissal will not be entertained if the particulars of the claim are founded upon a matter of opinion. It is not intended that the authority of the referee will be usurped as a result of a Claim for these offences.
The particulars upon which a claim is founded must be submitted by the club on behalf of the player to the Association within three days of the match. At the same time, the club is required to submit as an integral part of the Claim a video recording showing the incident, if such evidence is available.
The club must confirm, in writing, the source of the video recording at the time the Claim is lodged.
An appeal fee must be submitted with the claim for wrongful dismissal. The relevant fees are: -
First Team All Other Teams
Scottish Premier League Clubs: £1000 £500
Scottish Football League Clubs: £500 £250
All other clubs: £100 £50
The sanction(s) which arise from any sending off which is subject to a claim will be set aside until the investigation and/or consideration of the Claim of Wrongful Dismissal is completed.
Once the Claim of Wrongful Dismissal is lodged, the referee, in the first instance, will be requested to review the circumstances of the player’s sending off. If it is indicated by the referee that he is content with his decision to send the player off, the Claim will be dismissed automatically and not referred to the Review Panel. The sanctions will be re-applied with immediate effect and the appeal fee will be forfeited.
If the referee advises that the player should not have been sent off, the claim will be referred to the Review Panel.
The Review Panel, being a sub-committee of the Disciplinary Committee, will consider and investigate the claims.
The Review Panel shall have the power to uphold the Claim by expunging the offence from the player’s disciplinary record.
The appeal fee will be returned to the player’s club in the event that the Claim is upheld.
The decision resulting from the investigation and/or consideration of a Claim of Wrongful Dismissal is final and binding and shall not be the subject of appeal

Thanks to Auldyin on the KDS forum for a look at the SPL rules.