Poor planning and the difficulty of supplying the Mediterranean Expeditionary Force (MEF) certainly amplified the problems faced by General Ian Hamilton during the Gallipoli campaign, but the British (I use the term to cover all Empire forces here) ran into the same broad problems that pretty much all armies faced during the first half of the war. Namely; lack of an exploitation ability, lack of battlefield communication and troops who were neither properly trained or equipped for the fighting they faced. If the Allies couldn't succeed quickly, then the inevitable First World War problem would happen. Reinforcements would be rushed in and stalemate would ensue.

I'm going to ignore the question of whether the goal of the campaign was correct or even achievable, and focus more on what problems the British faced in trying to achieve that goal. Basically the idea was to use land forces to clear the coastal defences of the Gallipoli peninsula to allow Allied ships to clear the mines that blocked passage through the Dardanelles.

To do this Hamilton was given four divisions of infantry, (29th Division the only regular division, Royal Naval Division a real hodge podge of units made up of sailors, naval base men and reserves, the 1st Australian Division and the New Zealand and Australian Division [NZ&A Division]) about 80,000 men.

Instead of attacking at the narrowest part of the peninsula, Bulair, which was very heavily defended, Hamilton decided to land at Cape Helles in the south which was closer to the forts and where there were far fewer Ottoman units stationed, and which was further from reinforcements. Another attack was planned along the north coast at a place which became known as Anzac Cove. The attack in the north was intended to cross the peninsula in another narrow section and block off the reinforcement and escape of troops further in the south, whilst still removing the troublesome coastal forts. This in theory would only take a few days.

So why didn't it work?

Well to start with the troops Hamilton had were far from the best. The 29th Division was by far his best formation as it was made up of units that had been garrisoning various colonies before the war and was full of veteran troops. The Royal Naval Division was more or less a New Army division, created at the wish of Winston Churchill from naval reservists and volunteers who joined in 1914. It lacked experienced officers and NCOs and apart from some of its 3rd Marine Brigade, it had no campaign experience and little training. The two Dominion divisions were little better. Also raised from volunteers of 1914 they were enthusiastic but poorly led, trained and equipped. The Cambridge Military history of Australia goes as far as to say that "the 1st Division was probably the worst-trained formation ever sent from Australian shores." Although the rank and file troops were of good physical quality, their leaders were often too old and lacked campaign experience, and they suffered the same equipment deficiencies that all British forces did in 1915, particularly in machine guns, grenades, mortars and artillery. The NZ&A Division had all of the problems of the purely Australian division, with the added difficulty of being a composite force being led not by a Kiwi or Aussie, but by an English general, Sir Alexander Godley. This was put against three Ottoman divisions on the Peninsula, and with the recent memory of the Balkan wars the British vastly underestimated the fighting quality of Ottoman troops.

Any military operation is difficult, but amphibious landings are probably the hardest of all and there were problems at more or less every level of the actual operation. There weren't a lot of good maps, and what maps there were had to be copied, which inevitably turned out poor quality maps for most of the British forces, particularly for battalion commanders and below. Cooperation between navy and army wasn't particularly good either. Neither Hamilton nor Admiral John de Robeck were great communicators and de Robeck was apparently quite indecisive, leaving it to Hamilton to make plans that involved naval cooperation, such as command over the landing beaches, the landing order of units and stores. Naval gunnery has never really been a British strong point, and it showed at the landings. Some of this though was due to the difficulty of the terrain, as the flat trajectory of naval guns couldn't hit Ottoman positions on the rear of hills.

As for the troops, they ran into the obvious problems. Apart from parts of the 29th Division, command and control largely broke down. Particularly in the scrubby gullies of Anzac Cove, troops became mixed up from their units, officers got lost, became casualties or simply had no idea of what to do and troops lacked the discipline and knowledge to take advantage of the almost equal level of disorganisation amongst the Ottoman defenders. Once resistance stiffened men went to ground and trenches started to be dug. Due to the chaos and heavy casualties, particularly from unopposed Ottoman artillery, the attacks stalled. Even where they were successful British troops lacked the ability to exploit that success as either they lacked clear orders or were ordered to hold their current positions until the situation became clear. Once trenches had been dug though, they pretty much stayed there, despite the best efforts of both sides. Once the British attacks had been halted they never really moved again until the evacuations over the winter.

I'm basically of the opinion that after the first day the British lost any real chance at success, which was exceedingly slim to begin with. So TLDR;

Planning failures: Lack of intelligence in maps, positions, understanding of terrain (I haven't really emphasised enough how difficult it was, particularly at Anzac), lack of inter-service cooperation, lack of experienced staff officers, lack of training and experienced troops.

Logistical failures: Lack of suitable artillery. Again, I haven't really mentioned it enough but there artillery problems were severe. There wasn't much artillery, and what there was was mostly flat trajectory field guns, not high angle firing howitzers. Hamilton and his staff were constantly begging the War Office for more howitzers and high explosive ammunition, as they had not enough of either. Water was scarce on the peninsula and had to be rationed. Fresh food was more or less unavailable which, along with poor sanitary conditions, led to high rates of disease, particularly dysentery. Lack of modern weaponry. The Ottoman forces were being supplied with German grenades and mortars while the British had neither and were forced to improvise, famously with the 'jam tin bomb'. Even if the Ottomans didn't have a perfect doctrine for their use, they at least had them while the British did not. And all of this was at the end of a very long supply chain. Some food and water could be acquired from places closer by like Egypt, but most military supplies had to come from Britain and took weeks or months to arrive.

Planning and logistics always play a role in the outcome of a campaign, often a decisive one. Gallipoli is kind of a perfect storm of everything going wrong, including but not limited to planning and supply.