part 1: https://gist.github.com/laiso/c3009b11caa246c5f92e23a7f8b27b2d

ErrorHandlingInRxSwift2.swift

class ViewController: UIViewController {
    @IBOutlet weak var button: UIButton!
    
    private var viewModel: ViewModel!
    private let disposeBag = DisposeBag()
    
    override func viewDidLoad() {
        super.viewDidLoad()
        
        viewModel = ViewModel(buttonTap: self.button.rx.tap.asObservable())
        viewModel.item.asDriver(onErrorJustReturn: -1)
            .drive(onNext: { _ in
                print(1)
            })
            .disposed(by: disposeBag)
        
        viewModel.errorMessage.observeOn(MainScheduler.instance)
            .subscribe(onNext: { e in
                print("[ERROR]", e)
            })
            .disposed(by: disposeBag)
    }
}

struct ViewModel {
    let item: Observable<Int>
    let errorMessage: Observable<String>
    init(buttonTap: Observable<Void>, api: ItemAPI = ItemAPI(session: URLSession.shared)) {
        let errorSubject = PublishSubject<String>()
        errorMessage = errorSubject.asObservable()
        item = buttonTap
            .flatMapLatest { api.getItems() }
            .retryWhen {
                $0.map { error in
                    errorSubject.onNext(error.localizedDescription)
                }
            }
    }
}