How to compare institutions based on the difference between their predicted and observed values? I have predicted values from an OLS model. 
I am trying to identify if the predicted value is significantly different to the actual value for an observation. The actual value is a rate (not mean) based on the entire population's data for that observation. Each observation is an institution covering different population sizes. 
To create confidence intervals for the predicted value, I have constructed standard errors based on the population sizes of each institution.  
to determine statistical significance, do I also need to account for the confidence interval for the predicted value produced by the regression model? 
 A: The simple answer to your question is yes, if you want to know whether an observation is an "outlier" then you need to know the errors in both the model predictions and in the observations themselves.
You evidently seek a formula that will determine whether certain institutions are under-providing a type of surgery. If you proceed in this direction, however, you are entering dangerous territory. In your trek you will need more than advice from well-meaning strangers (as on this site) and more than a guidebook (as from a statistics textbook). You need experienced human guides, in the form of colleagues who have a deep understanding of the statistical issues and colleagues who understand the social and political ramifications of what you are trying to accomplish.
Here is a brief outline of some difficulties you face.
First, if your OLS model includes outliers, there are inherent problems with the model and with conclusions drawn from it. For one, the regression coefficients may be unduly affected by the outliers. Also, the differences between observed and predicted values may not have the well-behaved normal distributions needed for standard statistical tests. Identification of outliers is important in building a model and there are ways to assess them, but there is no formula that determines whether a particular observation is an outlier or not, just guidelines about which observations might need particular attention. 
Let's put aside that problem and consider issues that would arise even if you had a reliable model and wanted to see if a new, independent observation was well fit by the model.
The nature of your OLS model. Particularly if there are differences in the sizes of the populations served by the different institutions, OLS based on observed rates might not be the best analysis. Errors in estimating rates necessarily increase with smaller numbers of cases, so assumptions necessary for significance testing in OLS would not be met. This can be dealt with by generalized linear models (GLM) that deal with counts directly (in terms of numbers of surgeries, numbers of individuals with the disease, size of population--not simply rates). If you have reason to believe that there are two distinct and sufficiently large classes of institutions, high-surgery and low-surgery, you could even consider building a classification scheme to distinguish those classes. But either way this is now beyond OLS.
Adequacy of the linear model. Whether OLS or GLM, the assumption is that changes in the outcome variable are linearly related to changes in the predictors. For example, you include an "index of multiple deprivation" as a predictor. Why do you expect that this will be linearly related to the rate of a surgical procedure? How will you evaluate that assumption? Have potentially important variables been left out of the model? What about the age structures of the populations served? What about incentives for surgeons? (In the USA surgeons in some institutions are essentially salaried while in others they are compensated on a per-case basis. Were you analyzing USA data that difference might be important to include.) If you don't include enough predictors, any findings you make will be very easy targets for political counter-attack (see below).
Potential overfitting, particularly with several predictor variables. (And if you don't have several predictor variables for analyzing this situation, your model might not be adequate to start with.) A regression model with small errors in fitting a particular data set may not generalize well and may have larger errors when applied to other observations. You seem to have whole-population data rather than a sample, which might help, but there is the question of how well the particular regression coefficients may generalize, say, from year to year. So estimates of prediction errors should include correction for such "optimism" in model fitting.
Policy implications. You start with an assumption that some institutions are "under-providing" surgery. In over 40 years of working with surgeons, I've noticed that they really like to perform surgery. One might worry more whether some institutions are "over-providing" surgery. That crucial distinction needs to be addressed by clinical trials, not by analysis of surgery rates. For example, if you were analyzing prescriptions of antibiotics for colds you would want to be on the low-providing end of the distribution.
Political implications, in the broad sense of dealing with the institutions, the media, government officials, and the public. Are there members of the media or government officials who can be convinced by data presented in histograms? Even in that unlikely event, many members of the public will not understand histograms. If after your analyses you are convinced that there are institutions systematically under-providing surgery, you will need more compelling types of presentations. You also will need to make sure that your model and results are unassailable, as those whom you find to be "outliers" will almost inevitably fight back hard and will seize on any weakness in your analysis to counter-attack. Hence you need to make sure that your analysis is as well developed as possible and vetted by experts in this type of study before you go public.
