As far as i am concerned, the precautions are in need before taking delivery of bl. It should be checked for quantity, name of cargo, consignee and consignor. And most important one is its status (freight prepaid etc). You should inform the company before signing it. If all data on bl is mutually agreed by all parties, there is no danger of it. 

So, the dangers are before signing org bls, not during keeping it onboard

Hope this is helpfull

Normally there will be 3 sets of Original B/L which is signed by Master. It will be mentioned at the bottom of each of the original B/L. Now consider if the vessel is sailing and the cargo has been sold to the different buyer which will be endorsed by the previous owner of the cargo on the 2 sets of original B/L. But this will not reflect on the 1 set of original B/L which is with the Master. The issue arises with the Customs at the discharge port. As a part of the pre-arrival formalities, the ship is supposed to send a set of documents to the agent at the discharge port one among which will be the B/L. Now if the new buyer of the cargo presents only 2 /3 set of B/L to the custom office with the name of the new buyer and the Master has sent 1 original which has the name of the previous buyer, this can create lot of paperwork issues. Also banks also needs that the Accomplisehed B/L is endorsed on all the original sets of the B/L.