Do the residual plot and QQ plot look normal? I am doing linear mixed model and would like to check the assumptions using residual plot and QQ plot. Here is my code:
data1.frame <- read.delim("height.txt", fileEncoding="UTF-16")
lmer50      <- lmer(response ~ (1|jumper) + group*gender, data=data1.frame, REML=FALSE, 
                    na.action=na.omit)
plot(fitted(lmer50), residuals(lmer50))

For the residual plot, here is the output:  

qqnorm(data1.frame$response)
qqline(data1.frame$response)

For the qq plot, this is the output:  

Could I ask if both of them look normal? Can I apply linear mixed model in my rating scale data?
 A: Likert data simply cannot be normal.  Although in some cases it is safe enough to treat it as normal, it isn't actually ever normal and treating it as such is potentially dangerous.  
In addition to the points @Glen_b has made, your residual plot doesn't look good.  The residuals should be symmetrical (vertically) around the 0 line.  Either there is something seriously wrong with your model or you have strong skew in opposite directions at the two ends (this seems more likely).  This means that your model will be attenuated through much of its range (as you get closer to the ends, the predicted values will be closer to the grand mean than they should be), but then will overshoot the possible values if you were to move far enough out from the mean of X.  So in addition to your interval estimates being distorted, the model isn't even picking out your means correctly.  
You would do best to use a mixed ordinal logistic regression.  
A: Pretty obviously not normal. A step function is not a straight line. However, you also seem to be checking (unconditional) normality of the response, which is not assumed to be normal in a mixed model (you'd have some mixture of normals, depending on the fixed effects)
You clearly have discrete data. So your response's conditional distribution will be discrete, not normal.
This is what a Q-Q plot of normal residuals with sample size close to yours tends to look like:

The non-normality you will have in your conditional response is not automatically a big problem - it may or may not be. You don't seem to have strong skewness, for example, nor heavy tails and your sample size is largish.
Please describe your response in more detail. What is this "rating scale data"? (It sounds like it might be an ordinal scale.)
One thing you can do is use simulation to investigate the effect of this discrete scale on the inferences you wish to perform compared to having an actually normal error term.
