Can one compute confidence intervals for a census with high nonresponse rates? If a questionnaire was administered to an entire population (group of interest) and the response rate was 68% can the questionnaire results be generalized to the population (100%, including the 32% missing)? Can confidence intervals be used for the data subsets even though this is more like a census questionnaire?
 A: In general, no, you cannot do this.
More detail: The problem is that the 32% may be different from the 68%. If all you know is that they are missing then you have no way of saying in what way they may be different. But it's complex. With any missing data problem, even one with a census, one key thing is to determine (if you can) why there are missing data. The standard classification is: 
Missing completely at random (MCAR)- that is, there is no particular reason why they are missing. Perhaps coffee spilled on their records. Or perhaps a random computer glitch did not send them the questionnaire.
Missing at random (MAR: The reasons for the missingness are captured by data that you do have. E.g., it is known that people at both ends of the income scale are less likely to answer the phone which would give missing data on a phone interview. But if you know the income of people who don't respond, then the data may be MAR. 
Not missing at random (NMAR): Neither of the above.
If data is MCAR then your 68% results can be used "as is" as estimates of the population values. 
If data are MAR then there are various approaches; probably the most popular now is multiple imputation.
If data are NMAR then there is no perfect solution, but I have seen some work showing that multiple imputation works reasonably well unless the data are "REALLY NMAR" (I saw a presentation by Joe Schafer, who is one of the real experts on this).
