Core data, how to get NSManagedObject's ObjectId when NSFetchRequest returns NSDictionaryResultType?

Yes you can, using the very nifty but badly-documented NSExpressionDescription class. You need to add a properly-configured NSExpressionDescription object to the array of NSPropertyDescription objects you set via setPropertiesToFetch: for your NSFetchRequest.

For example:

NSExpressionDescription* objectIdDesc = [[NSExpressionDescription new] autorelease];
objectIdDesc.name = @"objectID";
objectIdDesc.expression = [NSExpression expressionForEvaluatedObject];
objectIdDesc.expressionResultType = NSObjectIDAttributeType;

myFetchRequest.propertiesToFetch = [NSArray arrayWithObjects:objectIdDesc, anotherPropertyDesc, yetAnotherPropertyDesc, nil];
NSArray* fetchResults = [myContext executeFetchRequest:myFetchRequest error:&fetchError];

You should then have a @"objectID" key in the the dictionaries you get back from your fetch request.

 NSFetchRequest *request = [[NSFetchRequest alloc] init];
    request.entity = [NSEntityDescription entityForName:@"yourEntity" inManagedObjectContext:context];
    request.sortDescriptors = [NSArray arrayWithObjects:[NSSortDescriptor sortDescriptorWithKey:@"title" ascending:YES], nil];
    request.predicate = nil;
    request.fetchLimit = 20;

    NSError *error = nil;
    NSArray fetchedResults = [context executeFetchRequest:request error:&error];

    NSLog(@"%@", [fetchedResults valueForKey:@"objectID"]);

Since your fetched results are already in an array why not pull them out with the valueForKey:@"objectID" ? Clean, simple only need one fetch request so you can pull all other data you need as well.