Yes you can handle with the catch operator like this and show alert as you want but firstly you have to import Rxjs for the same like this way

import {Observable} from 'rxjs/Rx';

return this.http.request(new Request(this.requestoptions))
            .map((res: Response) => {
                if (res) {
                    if (res.status === 201) {
                        return [{ status: res.status, json: res }]
                    }
                    else if (res.status === 200) {
                        return [{ status: res.status, json: res }]
                    }
                }
            }).catch((error: any) => {
                if (error.status === 500) {
                    return Observable.throw(new Error(error.status));
                }
                else if (error.status === 400) {
                    return Observable.throw(new Error(error.status));
                }
                else if (error.status === 409) {
                    return Observable.throw(new Error(error.status));
                }
                else if (error.status === 406) {
                    return Observable.throw(new Error(error.status));
                }
            });
    }

also you can handel error (with err block) that is throw by catch block while .map function,

like this –

...
.subscribe(res=>{....}
           err => {//handel here});

Update

as required for any status without checking particluar one you can try this: –

return this.http.request(new Request(this.requestoptions))
            .map((res: Response) => {
                if (res) {
                    if (res.status === 201) {
                        return [{ status: res.status, json: res }]
                    }
                    else if (res.status === 200) {
                        return [{ status: res.status, json: res }]
                    }
                }
            }).catch((error: any) => {
                if (error.status < 400 ||  error.status ===500) {
                    return Observable.throw(new Error(error.status));
                }
            })
            .subscribe(res => {...},
                       err => {console.log(err)} );