Learn Hardcore Japanese: toutyakusitabakari no nimotu ni mondai ga atta node, mise ni renrakusite koukansite moraimasita. - Because the package had just arrived and had an issue, I contacted the store and got it exchanged.

Vたばかり means “have just/recently V-ed,” but “recently” is fuzzy and subjective (minutes, hours, even a few days depending on context).
Vたところ means “have just V-ed right now/very immediately,” and often implies the result is fresh or the next step follows.
As a noun modifier, you use VたばかりのN (e.g., 届いたばかりの荷物). You generally don’t say VたところのN in this sense; instead, use it as a sentence: 届いたところです.

Is 到着したばかり natural for a package? Would 届いたばかり be better?

到着 is fine in shipping/logistics contexts (“arrival”), and appears on tracking pages.
In everyday conversation for a package that arrived at your place, 届く is more natural. So: 届いたばかりの荷物 or, if you mean the product inside, 届いたばかりの商品.
到着 is very common for planes, trains, shipments arriving at a hub; 届く emphasizes delivery to the recipient.

Why is there a の after 到着したばかり?

Why 荷物に問題があった? What does the particle に do here? Could I use で or は?

N に問題がある/あった is a fixed pattern meaning “there is/was a problem with N.”
に marks the entity that “has” the problem (the locus).
で would mean “at/during/with respect to the activity or setting,” e.g., 配送で問題があった (“There was a problem in/with the shipping process”), not the item itself.
は is a topic marker; you can say 荷物には問題があった, but the に is still needed. 荷物は問題があった feels off because it drops the necessary に.

Why not say 問題でした? What’s the nuance of 問題があった?

問題があった literally means “there was a problem,” an existential statement. It combines naturally with Nに (the thing that had the problem).
問題でした is “it was a problem” (categorical), but it doesn’t tie the problem to the package as neatly. For “there was a problem with the package,” prefer 荷物に問題があった.

Why use ので here? How is it different from から or ため?

ので gives a reason with a softer, more objective tone; it’s polite-friendly and sounds less blunt than から.
から is more direct and conversational: 問題があったから、店に連絡した.
ため(に) is more formal/written or “due to/for the sake of”: 問題があったため、店に連絡しました.
Before ので, plain form is fine (あったので). In formal writing you’ll also see ありましたので.

Why 店に連絡して? Why に and not を or と?

The standard pattern is 人・組織に連絡する = “contact someone/somewhere.”
と is used with 連絡を取る: 店と連絡を取る (“be in communication with the store”).
を is used if you treat 連絡 as the direct object in 連絡をする, but you still need 人に for the recipient: 店に連絡をする. The shorter 店に連絡する is most common.

Why two して in a row (連絡して交換して)? Is that okay?

Yes. The て-form chains actions in sequence or cause-effect: “(I) contacted the store and (then) got it exchanged.”
Japanese allows a subject shift across a て-chain when it’s clear: “I contacted (連絡して), (they) exchanged it for me (交換してもらいました).”
Alternatives: 店に連絡し、交換してもらいました (slightly more formal) or 店に連絡してから交換してもらいました (explicit “after”).

Where is the object of 交換して? Shouldn’t it be 荷物を?

It’s omitted because it’s obvious from context. Natural Japanese often drops repeated elements.
You can include it for clarity: 店に連絡して、荷物（商品）を交換してもらいました.
If the problem is with the item inside, 商品を is usually more accurate than 荷物を.

What exactly does 〜て(は)もらいました express? Why not 〜てくれました or just 交換しました?

〜てもらう = “have someone do X for me / get someone to do X,” highlighting your benefit/request. Here: “(I) got the store to exchange it (for me).”
〜てくれる = “someone kindly does X for me,” focusing on the doer’s kindness. You’d normally specify the subject: 店が交換してくれました or 店に連絡したら、交換してくれました.
交換しました would mean “I exchanged it (myself),” which is not the intended meaning if the store did the actual exchange processing.
Avoid 交換させました (“I made them exchange it”), which sounds coercive.

Would 交換していただきました be more polite? When do I use いただく vs もらう?

〜ていただく is the humble version of 〜てもらう and is more polite/formal: 交換していただきました.
Use 〜ていただく when speaking politely about someone’s favor (especially to outsiders or in business). With friends, 〜てもらう is fine.
For a request, you’d say 交換していただけますか (polite), vs 交換してもらえますか (less formal).

Should I repeat 店に before 交換してもらいました to mark who did the action?

You can say 店に交換してもらいました (marking the doer with に). It’s perfectly grammatical.
In the given sentence, it’s omitted to avoid repetition since 店に連絡して already set the context. Japanese often relies on context instead of repeating the agent.
If you want explicit flow without repeating 店に, you can say: 店に連絡したら、交換してもらいました.

What’s the difference between 交換する, 取り替える, and 返品する?

交換する: exchange one item for another (often the same product, e.g., defective -> new one).
取り替える: swap/replace parts or items; a bit more everyday and physical (e.g., 電池を取り替える).
返品する: return an item (give it back for a refund).
In this situation, if the store gave you a new unit for a faulty one, 交換してもらう is standard. If you returned it for a refund, 返品させてもらいました/返品しました.

Could I say 交換されました (passive)? Why or why not?

交換されました is passive and sounds report-like/impersonal (“It was exchanged”). In personal storytelling, Japanese prefers the beneficiary construction: 交換してもらいました.
Passive is okay in objective reports or when the agent is irrelevant: 不良品は交換されました.

If I want to say “I was able to get them to exchange it,” how do I change it?

Use the potential of もらう: 交換してもらえました (“I managed to get them to exchange it” / “they agreed to exchange it”).
Even more explicit: 交換に応じてもらえました.

Why 店に and not 店へ?

へ marks physical direction; 連絡する is not physical movement.
The fixed pattern is X に連絡する (contact X). So 店に連絡する is the natural choice.

Any nuance difference between 荷物 and 商品 here?

荷物 = the package/parcel itself (box, shipment).
商品 = the product/merchandise inside.
If the product was defective, 商品に問題があった is more precise; if the package was damaged (box crushed), 荷物に問題があった fits.