Either I am misinterpreting your plot or there is some problem. The fact that you have negative residuals for near 0 expected values implies that your model is predicting negative value. This should not be possible for logistic regression
models which only predict in the (0, 1) interval, unless you are using the log-odds output of the model in which case residual error should be undefined. Since logistic regression is a classification method, it is more useful to look at the confusion matrix first. You should also specify if the graph is based on the train data or a separate test set.
You are using a Likert scale or similarly defined ordinal dependent (and independent) variable and modeling it in the same way as a continuous variable. The debate of whether Likert scale can be modeled as a continuous numeric variable is a bit murky and can be summarized here:
http://www.theanalysisfactor.com/can-likert-scale-data-ever-be-continuous/
In practice, I tend to not have a problem with treating ordinal independent variables as numeric variables if there are at least five values and you are somewhat confident they are equally spaced on the spectrum of possible values -- that is, a difference between any two consecutive is approximately of equal magnitude. This practice is not grounded in theory, but experience has shown me that results tend to not be badly biased.
If this work is intended to be published, I suggest you either carefully justify your decision to use this method or look into alternative methods. EDIT: As suggested by @NickCox in the comments, ordered logit (or probit) regression would be a suitable alternative to deal with the ordinal response variable.
One consequence of treating the variables as continuous is that the residual plot can appear as a series of parallel lines, as your plot shows. This makes the typical pattern detection of the residual plot more difficult since the points clearly will not be randomly scattered.
As far as your plot is concerned, I believe it is acceptable. There is no clear curvature of the plot, and no fanning (i.e. no heteroscedasticity). They appear (to me) to form a roughly horizontal band if you take the density of points into account when forming the band. I would suggest plotting the absolute value of the residuals to help assess heteroscedasticity further.
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When looking at regression diagnostics, reading a half-normal plot of residuals is fairly similar to reading the top half of a Q-Q plot of residuals, at least when identifying lighter or heavier tails than anticipated. However if one tail is lighter and the other heavier, that may be less easy to identify in a half-normal plot (though much more or less skewness than expected will still show up as a wiggle)
(Half normal plots are sometimes used on estimated effects to identify "important" effects from "unimportant"; that doesn't seem to be what you have here)
In a GLM of course you don't expect the residuals to be actually normal unless the family was normal. The deviance residuals plot you show, where the expected "line" is actually a curve may be a little harder to judge; at least you have the "curve" to help you.