This can introduce a number of problems, like additional attenuation or cross talk. Splicing is to be avoided whenever possible, but I have seen this work in a pinch although I would never recommend it. They key is to use a cable certification tester (not just a continuity tester) to make sure it still passes your required standard (Cat5/5E/6) after splicing.
I would also be concerned about the manner of the splice. Twisting and electrical tape are not a reliable splicing method. Even if it is working properly initially, there is too much chance of problems to occur over time as the cables move slightly (temp changes, building vibrations, large vehicles driving by, etc).
The very first type of problem you can experience would be the inability to connect over the cable. Since it appears you can do so, then the next problem would be frame loss, often from corrupted frames that will get dropped when they fail a consistency check.
If you have real equipment on both sides of this link, you should be able to view the interface statistics and see how many frames are being dropped as well as the reasons.
When you use TIA/EIA-568B on both sides this is a straight through cable. The colors of the inner jackets don't really matter, much the same as it makes no difference to the operation of the network if you use a network cable with a black or yellow outer jacket.
However, the standard is in place for a real reason, and that is that the cabling system should be implemented in a standard way so that anyone who works on it will intuitively understand what they are working on.
For instance, imagine if someone used your reversed wiring in a real environment, left, and you were now troubleshooting a cabling issue at that site. On inspection, you determine the cable is damaged and it need to be re-terminated on one side and did so with the standard TIA/EIA-568B. After doing so, the cable still will not work.
It isn't because your termination is bad, but because the cable is now a rolled cable. You may waste additional time/resources on trying to re-terminate the cable additional times. Unless you use a cable tester, you may not easily figure out that the cable is now a rolled cabled.
Ultimately, this potentially causes more problems/downtime and isn't really justifiable by any possible reason the original person may have had to not follow the standard.
Old answer (thinking the OP was talking about using TIA/EIA-568B on one side and the reverse on the other):
What you are describing is what is often referred to as a "rolled" or "rollover" cable. Pin 1 connects to pin 8 on the other side, pin 2 to pin 7, etc.
This type of cable would not work for network communications, but is used by many vendors for serial communication, such as console port access.
Best Answer
This is more or less to be expected - alligator clips aren't Cat anything, so probably the link training gave up and the link fell back to Fast Ethernet (not standard but not uncommon). Another possibility is that there's a bad contact somewhere and one of the pairs didn't link, also causing a fallback to FE.
If you can't replace the cable, use a splice box to reattach the ends.