The issues with MtGox are specific to MtGox having used shoddy code years ago that came back to bite them. They knew there was a problem with their trade platform, yet did not take sufficient action to fix it- and over time theft using that exploit drained their reserves and bankrupted them. What we have seen with MtGox is the first ever cryptocurrency 'bank run'. MtGox is not the only exchange out there- I personally am using Coinbase to get in and out of bitcoin as needed while trading dogecoin for bitcoin.
Yes it has its issues, but it also has a lot of neat capabilities too. The wallets for bitcoin can integrate with any other system- it is all electronic, has little to no fees, and doesn't rely on any kind of central processor like paypal does.
On top of that, bitcoin payments cannot be reversed or charged back- once you send a payment it is gone unless the person you send it to is generous enough to send it back.
Really the biggest hinderance to it is a lack of understanding of how it actually works and widespread usage to stabilize its value. Dogecoin is the same way.
I would accept either method- bitcoin or dogecoin as valid payment. Mind you it would have to be processed manually on my end, but that isn't a big deal. If enough people start using it, I'll add an automatic payment handler for it. The wallet software provides a JSON API for doing so if you choose to.
As for the fraud issues, the bulk of them come from people being careless in handling it or trying to treat it like something it isn't. When exchanging it for Fiat for instance, always go with a reputable exchange or escrow service. Fiat transactions can usually be charged back, cryptocurrency transactions can't. Having a neutral party in between helps avoid complications with this happening and keeps both parties honest.
Mining itself isn't fraud at all other than the usual bad apples using botnets to do it. All you are doing is using your CPU/GPU/ASIC power to solve hashes that contribute to forming a valid block. Each block is a page in a ledger of transactions that describe the entire network from the very beginning till now, they don't actually store the coins themselves because the coins don't actually exist.
So what happens when you make a transaction is it is sent to the miners, who code it into the blocks, and when a block is accepted by the blockchain that transaction becomes a part of the permanent record- the blockchain contains every two or more party transaction in the history of the entire network. Exceptions to this include transactions that happen within a single exchange or service and are not broadcast out to the network. After a sufficient number of blocks have been made that contain the same transaction, the transaction is considered permanent and indisputable.
Now to keep your bitcoins from getting stolen, use an OFFLINE wallet. The standard wallet software creates a private key to identify the wallet, and then generates public keys for transaction addressing. Keeping a secure backup of this private key is absolutely critical to the safety of your bitcoins, and at all times your bitcoins should be returned to your wallet when not actively being used. To date there is no known method of stealing from an offline wallet, but online wallets and exchanges can easily be hacked or can suffer from stability problems like MtGox is experiencing. Effectively everyone who was storing their bitcoin at MtGox just lost their bitcoin, but those who were smart and withdrew it to local wallets didn't lose a thing.
When I heard about this, I was laughing my butt off. I know it sounds harsh, but c`mon, the programming behind bitcoin puts too much trust in the hands of anonymous people (whom no one knows they are, and thus there is no security)
Would you trust a complete stranger to hold your suitcase (with no lock) filled with $5,000 of your hard earnt cash?
On the contrary- bitcoin transactions have more trust to them than fiat transactions. Anyone can steal your credit card info and drain your bank account, or buy something expensive and then dispute the charge. With bitcoin that's not possible- they would have to first gain control of your wallet and send those bitcoins out to another wallet, resulting in a transaction visible on the blockchain which can in fact be tracked. There is no chargebacks at all anywhere in the system.
Now if you were leaving your cryptocurrency on an exchange platform or in an online wallet service, THEN you are leaving your life savings in the hands of a total stranger and trusting them to not help themselves.
For people who are actively trading these currencies- the markets behave similar to Forex, but much wilder from lack of regulation, it is sort of unavoidable to leave some or all of it in an exchange for fast access when trading. Everyone else should always keep it in a local wallet and have multiple backups of the private key.