Animate tacky light decorations
MATLAB, 255 210 bytes
This is my first golf, so there are probably improvements to be made.
Thanks to Luis for helping me save 45 bytes :)
function f(n,m)
c=dec2bin(1:6)-48;r=1;p=c(r,:);x=zeros(1,n*m,3);x(:,:,1)=1;while 1
x=circshift(x,[0,1,0]);if rand&gt;0.94;r=randi(6);end
x(1,1,:) = c(r,:);imagesc(permute(reshape(x,n,m,3),[2 1 3]));pause(1/40);end

Explanation:
c=dec2bin(1:6)-48  % c is the colormap
r=1;p=c(r,:);                % p is color number r (starting at 1) from the colormap c
x=zeros(1,n*m,3);x(:,:,1)=1; % 2D matrix in the third dimension. The first layer is 1
while 1                      % while true
x=circshift(x,[0,1,0]);      % shift the vector horizontally along the second dimension
if rand()&gt;0.94;              % 5 percent chance of changing color
k=randperm(6);k=k(k~=r);r=k(1); % Create a vector with color numbers 1..6. Discard the current color, and choose the first color
x(1,1,:) = c(r,:);           % The first light gets color number r
imagesc(permute(reshape(x,n,m,3),[2 1 3]));  % Reshape the vector so that it's a 3D matrix
% Permute it so that the dimensions are correct
% Use imagesc to display
pause(1/40)  % 0.025 seconds pause

Unfortunately, this doesn't save the animation, it just runs it. In order to save it I either need a screen capture program, or rewrite it all using imwrite. Instead, I'll provide two pictures showing different times, for n=15,m=30.